DS From Forums

8/6/2019 DS From Forums

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D S Solution from Forums

1. Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail ( imile =1.6km rounded to nearest tenth)

1. Pei walked the distance at an average rate of less than 6.4 km/hr.2 .On average it took Pei more than 9 minutes per km to walk the distance .1. At most, Pei walked 12.8km in 2 hours. Since the trail is 16km long, then we know thatPei took more than 2 hours. Therefore, statement 1 is sufficient

2. At the fastest, Pei walked 1 km in 9 minutes. Then to walk 16km, the Pei needs 144minutes, which is more than 2 hours. Therefore, statement 2 is sufficient

2. Is 1/x^5 > y/(y^6+1)?

(1) x=y --> is ? Two cases:

A. --> cross multiply and as for negative : and flip the sign(because of would be NO.

B. --> cross multiply and as for positive both and are positive remain the

sign. The question becomes: is ? --> is ? In this case the answer would beYES.

(2) y>0. Clearly insufficient as no info about .

(1)+(2) As from (2) then we have case B and the answer is YES. Sufficient.

negative ). The question becomes: is ? --> is ? In this case the answer Answer: C.

3. A certain alloy contains Lead , copper and tin. how many pounds of tin are in 56 poundsof the alloy

S1 By weight the alloy is 3/7 lead and 5/14 copper

S2 By weight the alloy is 6 parts lead and 5 parts copper Weight of Tin - T lbsWeight of Copper - C lbsWeight of Lead - L lbs

T+C+L=56 lbs of the alloy



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Q: T=?

S1: By weight the alloy is 3/7 lead and 5/14 copper

L=3/7*56

C=5/14*56T=56-(3/7*56+5/14*56).Sufficient.

S2: By weight the alloy is 6 parts lead and 5 parts copper Alloy is y parts Tx be the multiplier 6x+5x+yx=5611x+yx=56y,x can have many values. Not sufficient.

Ans: "A"4. GO 4; If k is an integer and 0.0010101 x 10^k is greater than 1000, what is the least

possible value of k?(a) 2(b) 3(c) 4(d) 5(e) 6

4. OG QR. In the xy plane, point (r,s) lies on a circle with center at the origin. What is thevalue of r^2+s^2?

(1) The circle has radius 2(2) The point (√2,-√2) lies on the circle.

I have problem with the option 2

THEORY:In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the setof all points (x, y) such that:



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This equation of the circle follows from the Pythagorean theorem applied to any point onthe circle: as shown in the diagram above, the radius is the hypotenuse of a right-angledtriangle whose other sides are of length x-a and y-b.

If the circle is centered at the origin (0, 0), then the equation simplifies to:

BACK TO THE ORIGINAL QUESTION:In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the

value of ?

Now, as then the question asks about the value of radius^2.

(1) The circle has radius 2 --> radius^2=4. Sufficient.

(2) The point lies on the circle --> substitute x and y coordinates of a point in--> . Sufficient.

Answer: D.5. OG. QR. 27: A collection of 36 cards consists of 4 sets of 9 cards in each set are

numbered 1 through 9. If one cadrd has been removed from the collection, what is thenumber on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.(2) The sum of the numbers on the remaining 35 cards is 176.

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through9. If one cadrd has been removed from the collection, what is the number on that card?



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(1) The units digit of the sum of the numbers on the remaining 35 cards is 6 --> we canget the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get whichcard should be removed so that the new sum to have the units digit of 6 (as cards are from

1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here.Sufficient.

Answer: D. [Bnnuel]

6. If x and y are positive intergers, what is the remainder when 10^x+y is divided by y?

(1) x=5(2) y=2

--> so we basically need the remainder upon division 10^x by y (as in

10^x+y the second term y is divisible by y itself then only the first term matters for

remainder).

(1) x=5 --> need the value of y. Not sufficient.

(2) y=2 --> as x is a positive integer then 10^x is an even number and 10^x=even divided

by 2 yields the remainder of zero. Sufficient.

Answer: B. [Bunnel]7. If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers.(2) n and 2^3 are each divisible by the same number of positive integers.

Finding the Number of Factors of an Integer

First make prime factorization of an integer , where , , and are primefactors of and , , and are their powers.

The number of factors of will be expressed by the formula .NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450:



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Total number of factors of 450 including 1 and 450 itself isfactors.

For more on number properties check: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

If n is an integer, then n divisible by how many positive integers?

(1) n is the product of two different prime numbers --> n=ab, where a and b are primes, so# of factors is (1+1)(1+1)=4. Sufficient.

(2) n and 2^3 are each divisible by the same number of positive integers --> 2^3 has 4different positive factors (1, 2, 4, and 8) so n has also 4. Sufficient.

Answer: D.8. OG DS 62: In the equation x^2+bx+12=0,x is a variable and b is a constant. What is the

value of b?(1) x-3 is a factor of x^2+bx+12.(2) 4 is a factor of x^2+bx+12=0

You don't really need Viete's formula for the roots of a quadratic equation.

(1) x-3 is a factor of x^2+bx+12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of

the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.(2) 4 is a factor of x^2+bx+12=0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

Answer: D.9. QR DS 66

If the average (arithmetic mean) on n consecutive odd integers is 10, what is the least of the integers?(1) The range of the n integer is 14.

(2) The greatest of the n integers is 17

Odd consecutive integers is an evenly spaced set. For any evenly spaced set the mean

equals to the average of the first and the last terms, so in our case

--> . Question:

(1) The range of the n integers is 14 --> the range of a set is the difference between the

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largest and smallest elements of a set, so --> solving for --> .Sufficient.

(2) The greatest of the n integers is 17 --> --> --> .Sufficient.

Answer: D.10.

QR DS 70K is a set of numbers such that

(i) If x is in K, then -x is in K, and(ii) if each of x and y is in K, then xy is in K

Is 12 in K?

(1) 2 is in K

(2) 3 is in K 1) 2 is in K --> according to (i) -2 is n K --> according to (ii) -2*2=-4 is in K -->according to (i) -(-4)=4 is in K and so on. Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ...are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(2) 3 is in K --> according to (i) -3 is n K --> according to (ii) -3*3=-9 is in K -->according to (i) -(-9)=9 is in K and so on. Thus we know that 3, -3, -9, 9, 27, -27, 81,-81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don'tknow. Not sufficient.

(1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 mustalso be in K. Sufficient.

Answer: C.

Yes, for ANY two numbers in the set their product is also in the set.11.

QR DS 79If m and n are nonzero integers, is m^n an integer?(1) n^m is positve(2) n^m is an integer.

(1) n=-2, m=2; n^m=(-2)^2=4. +ve;

m^n=(2)^-2=1/4=0.25. Not an integer

n=1; m=1; n^m=1^1=1; +ve

m^n=1^1=1; Integer.

Not Sufficient.



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(2) n=-2, m=2; n^m=(-2)^2=4. integer;

m^n=(2)^-2=1/4=0.25. Not an integer

n=1; m=1; n^m=1^1=1; integerm^n=1^1=1; Integer.

Not Sufficient.

Combining both;

n=-2, m=2; n^m=(-2)^2=4. integer and +ve;

m^n=(2)^-2=1/4=0.25. Not an integer.

n=1; m=1; n^m=1^1=1; integer and +vem^n=1^1=1; Integer.

Ans: "E"

If m and n are nonzero integers, is m^n an integer?

If n is a positive integer then m^n will be an integer for any value of m (taking into accountthat both are nonzero integers).If n is negative then m^n will be an integer if and only m=1 or m=-1, for example: (-1)^(-2)=1/(-1)^2=1

So basically we are asked: is n positive or m=|1|?

(1) n^m is positive --> either m=even (and in this case n can take any value) or n=positive (andin this case m can take any value). Not sufficient.

(2) n^m is an integer --> either m=positive (and in this case n can take any value) orm=negative and in this case n=1 or -1. Not sufficient.

(1)+(2) If n^m=(-1)^2=positive integer , then the answer will be NO as m^n=2^(-1)=1/2 but ifn^m=1^2=positive integer , then the answer will be YES as m^n=2^1=2. Not Sufficient.

Answer: E.[Bunnuel]

12

.qr ds 86

If m and n are consecutive positive integer, is m greater than n?

(1) m-1 and n+1 are consecutive positive integers

(2) m is an even integer

If m and n are consecutive positive integers, is m greater than n?



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(1) m-1 and n+1 are consecutive positive integers --> m>n, if m were less than n than m-1(integer less than m) and n+1 (integer more than n) wouldn't be consecutive. Sufficient.

(2) m is an even integer. Clearly insufficient.

Answer: A.13

.QR DS 87

If k and n are integers, is n divisible by 7?

(1) n-3 = 2k

(2) 2k -4 is divisible by 7

Is there any easier approach than official guide.

If k and n are integers, is n divisible by 7?

(1) n-3 = 2k --> n=2k+3, now if k=1 then n=5 and the answer is NO but if k=2 then n=7 and theanswer is YES. Not sufficient.

(2) 2k -4 is divisible by 7 --> 2k-4=7x, for some integer x --> k=(7x+4)/2. Clearly insufficient asthis statement talks only about k.

(1)+(2) As from (2) k=(7x+4)/2 then from (1) n=2k+3=7x+4+3=7(x+1) --> n is a multiple of 7.Sufficient.

Answer: C.

13.

GMAT PREP

are positive integers p and q both greater than n

(1) p-q is greater than n

(2) q>p

Given: and . Question: is and ?

(1) . Clearly insufficient.

(2) , no info about . Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction):

--> . As given that both and are positive then they are greater than

negative . Sufficient.



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Answer: C.

14.

90. Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3

(2) n is odd

The point here is that is some particular number.

Two statements cannot narrow the possible values of so that we can arrive to one answer:

YES or NO. Which means statement(s) are insufficient.

For example:

If , then the answer would be - YES, but if, then the answer would be - NO.

15.

89. If x+y+z > 0, is z > 1 ?

1) z > x + y + 1

2) x + y + 1 < 0

this is a question from OG 10, could someone please explain this. The explanation in the OG is

not clear enough.

Thanks,

Eddy

Welcome to Gmat Club Eddy!

Note that:

You can only add inequalities when their signs are in the same direction:

If and (signs in same direction: and ) --> .

Example: and --> .

You can only apply subtraction when their signs are in the opposite directions:

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If and (signs in opposite direction: and ) --> (take the sign of the

inequality you subtract from).

Example: and --> .

Back to the original question:

If x+y+z > 0, is z > 1?

(1) z > x + y + 1 --> as the signs are in the same direction we can add two inequalities:

--> --> , so z may or may not be more than 1. Not

sufficient.

(2) x + y + 1 < 0 --> as the signs are in the opposite direction we can subtract two inequalities:

--> --> . Sufficient.

Answer: B.

Hope it's clear.

16

.91. In the figure above, segments RS and TU represent two positions of the same ladder leaning

against the side SV of a wall. The length of TV is how much greater than the length of RV?

(1) The length of TU is 10 meters.

(2) The length of RV is 5 meters.

is a right-angled triangle with angles 45-90-45.

Ratio of its sides



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is a right-angled triangle with angles 30-90-60.

Ratio of its sides

(1)

TU=RS=10

Find TV-RV

Sufficient.

(2)

RV=10

Find TV-RV

Sufficient.

Ans: "D"

17.

Days Prior toDeparture

Percent of Package Price

46 or more10%

45 - 3135%

30 - 1650%

15 - 5

65%

4 or fewer 100%

93. The table above shows the cancellation fee schedule that a travel agency uses to

determine the fee charged to a tourist who cancels a trip prior to departure. If a tourist

canceled a trip with a package price of $1,700 and a departure date of September 4, on what



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day was the trip canceled?

(1) The cancellation fee was $595 --> cancellation fee is 595/1700=35% of a package price, so

the trip was canceled from 31 to 45 days prior to 4th of September. Not sufficient.

(2) If the trip had been canceled one day later, the cancellation fee would have been $255

more --> $255 is 15% of of a package price, so the trip was canceled either 31 or 16 days prior

to 4th of September (15% change is from 35% to 50% and from 50% to 65%). Not sufficient.

(1)+(2) The trip was canceled 31 days prior to 4th of September. Sufficient.

Answer: C.

18.

92. Is the integer x divisible by 36?

(1) x is divisible by 12(2) x is divisible by 9

Prime factors of

So if x is divided by a number whose factors at least comprise of all the prime factors of 36;

i.e. two 2's and two 3's then x will be divisible by 36.

1.Prime factors of 12 = 2^2*3

So; only two 2's and one 3. We require 2 two's and two 3's for the number to be divisible by 36.

Not Sufficient.

2.Prime factors of 9 = 3^2

So; only two 3's. We require 2 two's and two 3's for the number to be divisible by 36.

Not Sufficient.

Combining both;

x is divisible by; 2^2*3*3^2

The factors comprise of at least two 2's and two 3's. Must be divisible by 36.

Sufficient.

Ans: "C"

19.

107. The sequence s1, s2, s3,.....sn,...is such that for all integers

. If k is a positive integer, is the sum of the first k terms of the sequence greater than



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?

1) k > 10

2) k < 19

If you notice, the sum is simply given by Sn = 1 -1/(n+1) = n/(n+1). hence S9 = 9/10. Addingfurther terms only increases the sum - hence S10 > S9 etc...

1) k>10, clearly sufficient as S10>9/10 = S9

2) k<19, cant say much K can be 1 = 1/2<9/10 but K=11 makes 11/12>9/10

Hence A

I am not a master in choosing the right number, but as i read & practising the same ... Choose

the numbers which are closer to the lowest range & Highest range first.

Example:

(1) K > 10.The lowest range number here is: 11. If 11 is sufficient then take 12. If 12 is also sufficient find

out if you can make a generalized statement as Sufficient?

The highest range number is: Infinity

(2) K < 19

The lowest range number (according to problem specificaitons) is: 1

The highest range number is: 18

Cheers!

Ravi

20.

For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the

median?

1) If the n numbers in the set are listed in increasing order, then the difference

between any pair of successive numbers in the set is 2.

2) The range of n numbers in the set is 2(n-1).

1. it's clear it is a set with consecutive even numbers => median will always equal to the

mean.

sufficient

n=3

x,x+2,x+4



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(1)+(2) From (1) # of guests who ordered both dessert AND coffee is 45 and from (2)0.9*(coffee)=45 --> (coffee)=50. Sufficient.

Answer: C.22.

QR. DS. 122.If 2 different representatives are to be selected at random from a group of 10employees and if p is the probability that both representatives selected will be women is p>1/2?(1) More than 1/2 of the 10 employees are women.(2) The probability that both representatives selected will be men less than 1/10.

What is the probability of choosing 2 women out of 10 people and this should be

. So we have --> this is true only when . (w # of women )

So basically question asks is ?

(1) not sufficient.

(2) --> --> , not sufficient

(1)+(2) , not sufficient

Answer E.22.

OG 120. The annual rent collected by a corporation from a certain building was x percentmore in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rentcollected by the corporation from the building more in 1999 than in 1997?

1) X is greater than Y2) xy/100 is less than x-y

I'm hoping that someone can elaborate on the number property that gives answer b.Rent in 1997 - ;

Rent in 1998 - ;

Rent in 1999 - .

Question is true? --> -->



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true?

(1) , based on this information we can not conclude whether is true or not. Not sufficient.

(2) , directly states that the equation we were testing is true. Sufficient.

Answer: B.

, cancels out. Then .

, 1 cancels out --> , multiplu by 100 both

sides --> , rearrange --> .

23.

OG. 63. Stores L and M each sell a certain product at a different regular price. If bothstores discount their regular price of the product, is the discount price at Store M less thanthe discount price at Store L ?

(1) At Store L the discount price is 10 percent less than the regular price; at Store M thediscount price is 15 percent less than the regular price.(2) At Store L the discount price is $5 less than the regular store price; at Store M thediscount price is $6 less than the regular price.

1)

Product Price @ L= 100After Discount = 90Product Price @ M= 100After Discount = 85M's Price after Discount < L's price after discount.

Product Price @ L= 50After Discount = 45Product Price @ M= 100

After Discount = 85L's Price after Discount < M's price after discount.

Not Sufficient.

(2)



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Product Price @ L= 100After Discount = 95Product Price @ M= 100After Discount = 94

M's Price after Discount < L's price after discount.

Product Price @ L= 50After Discount = 45Product Price @ M= 100After Discount = 94L's Price after Discount < M's price after discount.

Not Sufficient.

Combing both;5 = 0.1L; L=50; After discount: 456 = 0.15M; M=40; After discount: 34M's price after discount < L's price after discount.

Sufficient.

Ans: "C"

Stores L and M each sell a certain product at a different regular price. If both storesdiscount their regular price of the product, is the discount price at Store M less than thediscount price at Store L ?

Let the regular price of a certain product at store L be and the regular price of a certain product at store L be .

If the rates of discounts were and then the prices would become: ) and. Question: is .

(1) At Store L the discount price is 10 percent less than the regular price; at Store M thediscount price is 15 percent less than the regular price --> and --> no infoabout the initial prices - and , hence not sufficient.

(2) At Store L the discount price is $5 less than the regular store price; at Store M the

discount price is $6 less than the regular price --> and .



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Not sufficient.

(1)+(2) As from (1) and from (2) then , andsimilarly as from (1) and from (2) then , --

> we have all information needed. Sufficient. ( ).

Answer: C. [BUNNUEL]24.

OG. 67. In a survey of 200 college graduates, 30 percent said they had received studentloans during their college careers, and 40 percent said they had received scholarships.What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?

(1) 25 percent of those surveyed said that they had received scholarships but no loans.

(2) 50 percent of those surveyed who said that they had received loans also30 percent received student loans --> 200*0.3=60 graduates received loans;40 percent received scholarships --> 200*0.4=80 graduates received loans;

200={loans}+{scholarships} - {both}+{neither} --> 200=60+80-{both}+{neither} -->

{neither}=60+{both} . Question: {neither}=?

As {neither}=60+{both} then we should calculate # of students who received both loansand scholarships.

(1) 25 percent of those surveyed said that they had received scholarships but no loans -->

{scholarships} - {both}=80 - {both}=0.25*200=50 --> {both}=80-50=30 -->{neither}=60+{both}=60+30=90 . Sufficient.

(2) 50 percent of those surveyed who said that they had received loans also said that theyhad received scholarships --> 0.5*{loans}={both} --> 0.5*60=30={both} -->

{neither}=60+{both}=60+30=90 . Sufficient.

Answer: D. [BUNNUEL]25.

OG. 121. In the xy-plane, region R consists of all the points (x,y)such that 2x + 3y ≤ 6. Is the point (r,s) in region R ?(1) 3r + 2s = 6(2) r ≤ 3 and s ≤ 2

Though the solution provided by shrouded1 above is perfectly OK, it's doubtful that can be done in 2-3 minutes.



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So I'd say the best way for this question would be to try boundary values.

Q: is 2R+3S ≤6

(1) --> very easy to see that this statement is not sufficient:If and then , so the answer is YES;If and then , so the answer is NO. Not sufficient.

(2) and --> also very easy to see that this statement is not sufficient:If and then , so the answer is YES;If and then , so the answer is NO.

Not sufficient.

(1)+(2) We already have an example for YES answer in (1) which valid for combinedstatements:If and then , so the answer is YES;

To get NO answer try max possible value of , which is , then from (1) --

> , so the answer is NO. Not sufficient.

Answer: E.

Hope it's clear.26.

OG. 124. The table above shows the results of a survey of 100 voters who each responded“Favorable” or “Unfavorable” or “Not Sure” when asked about their impressions of Candidate M and of Candidate N. What was the number of voters who responded“Favorable”for both candidates?

(1) The number of voters who did not respond “Favorable” for either candidate was 40.(2) The number of voters who responded “Unfavorable” for both candidates was 10.

Voters responded favorable for at least one candidates = 40+30-x = 70-x (x representthe # of voters who responded favorable for both candidates)

(1) The number of voters who did not respond “favorable” for either candidate was 40 -->



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The voters responded favorable for at least one 100-40=60=70-x --> x=10. Sufficient.

(2) The number of voters who responded “unfavorable” for both candidates was 10.Clearly not sufficient.

Answer A.27.

128. A school administrator will assign each student in a group of n students to one of mclassrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of them classrooms so that each classroom has the same number of students assigned to it?

(1) It is possible to assign each of 3n students to one of m classrooms so that eachclassroom has the same number of students assigned to it.(2) It is possible to assign each of 13n students to one of m classrooms so that each

classroom has the same number of students assigned to it.The Question is If N/M is an integer ?

(1) 3N/M is an integer Case 1 - N=15 M=3 it is clearly an integer when we substitute in above equ.Case 2 - N=14 M=6 Satisfy the statement 2 but doesn't work for above equ.Therefore Insuff.

(2) 13N/M= integer

13 is a prime number and since m is less than 13 therefore for this statement to hold true, N/M has to be integer. Hence Sufficient.

I hope that helps.

Basically the question asks whether (# of students) is a multiple of (# of classrooms),

or whether , because if it is then we would be able to assign students toclassrooms so that each classroom has the same number of students assigned to it.

Given: .

(1) It is possible to assign each of 3n students to one of m classrooms so that each

classroom has the same number of students assigned to it --> , from this

we can not say whether . For example indeed might be a multiple of (and ) but also it as well might not be ( and ). Not sufficient.

(2) It is possible to assign each of 13n students to one of m classrooms so that each



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classroom has the same number of students assigned to it --> , now as

given that then 13 (prime number) is not a multiple of , so to be aninteger the must be multiple of . Sufficient.

Answer: B. [BUNNUEL]28.

133. Are all of the numbers in a certain list of 15 numbers equal?(1) The sum of all the numbers in the list is 60.(2) The sum of any 3 numbers in the list is 12.

(1) The sum of all the numbers in the list is 60 --> clearly insufficient.

(2) The sum of ANY 3 numbers in the list is 12 --> as the sum of ANY 3 numbers is 12then ALL numbers must equal to 12/3=4, because if not all the numbers equal to 4, thenwe could pick certain set of 3 numbers so that their sum is not 12. Sufficient.

Answer: B. [BUNNUEL]

The numbers can be any set of 15 numbers that add up to 60!

Not sufficient

Statement 2:Out of 15, if we pick any 3 the sum is 12.Suppose we pick three numbers x y and z. Given x + y + z = 12

Now we replace any of the three numbers with another number. Say 'q'

q + y + z = 12 [Given]

So q = x ... same way q = y and q = z!This can be extended to all the numbers in the set.Thus they're all equal!

Sufficient!

Ans: 'B'29.

161. Beginning in January of last year, Carl made deposits of $120 into his account on the15th of each month for several consecutive months and then made withdrawals of $50from the account on the 15th of each of the remaining months of last year. There were



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no other transactions in the account last year. If the closing balance of Carl’s account for May of last year was $2,600, what was the range of the monthly closing balances of Carl’s account last year?

(1) Last year the closing balance of Carl’s account for April was less than $2,625.(2) Last year the closing balance of Carl’s account for June was less than $2,675.

this is not a very tough 750 lvl question. Bunuel showed the elaborate way of solving the problem. Since it is a DS question, you actually do not need to calculate that much either.From 1) We know that Carl deposited money in May (and thus in the previous months).However, we do not know how long he continued depositing. From 2) We know that hewithdrew money in June, but it does not say from when he started withdrawing.Combining both, by subtracting 120 for each previous months from May and alsosubtracting 50 for the coming months we will get figures. From there we can find the

range.[BUNNUEL]To find the range we should know:A. Balance before he started depositing, initial balance = x (we know that there wasinitial balance because for may balance was 2600 and maximum amount he coulddeposited for this period is: 5 months*120=600).B. Till what month he deposited $120.C. From which month he started withdrawing $50.

(1) April balance< 2625 --> he deposited in May (Because if he didn't then April balance=2600+50=2650 and we know that in April balance was<2625).So for may balance=2600=x(initial balance)+5months*120 --> x+600=2600 --> x=2000.We know initial balance, but we still don't know: till what month he deposited $120 andfrom which month he started withdrawing $50 Not sufficient

(2) June balance < 2675 --> he didn't deposited in June --> he withdrawed in June (if hedeposited, in June deposit would be May balance 2600+120=2720>2675) Not sufficient

(1)+(2) we know:Initial balance: x=2000Till what month he deposited $120: till MayFrom which month he started withdrawing $50: from June



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Sufficient C.30.

If n is a positive integer, what is the tens digit of n ?(1) The hundreds digit of 10n is 6.(2) The tens digit of n + 1 is 7.

If n is a positive integer, what is the tens digit of n ?

(1) The hundreds digit of 10n is 6.Multiplication by 10 will shift all digits one to the left. Ten's digit of n must be 6.

e.g.n=4324324242468<- 6 in tens place10n=43243242424680<-hundred's digit in 6 because 0 occupied the units place and restall of digits moved 1 to the left.

n=69<-6 in tens place10n=690<-6 in hundreds place

Sufficient.

(2) The tens digit of n + 1 is 7.n=69

n+1=70<-tens digit of n+1 is 7 when tens place of n=6

n=73n+1=74<-tens digit of n+1 is 7 when tens place of n=7

Not Sufficient.

Ans: "A"31.

173. if arc pqr above is a semicircle, what is the length of diameter pr ?

1) a=42) b=1

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image.JPG [ 5.73 KiB | Viewed 306 times ]

D.

let pq = xx^2 = 4 + a^2 ---- (i)

similarly, if qr = y

y^2 = 4 + b^2 ---- (ii)

as triangle pqr is right angle traingle,

x^2 + y^2 = (a + b) ^2 or 4 + a ^2 + 4 + b^2 = a^2 + b^2 + 2*a*b or ab = 4

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