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### Transcript of GMAT Questions

Question 1: A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm?

The question given below is a Math problem in Algebra and requires framing a couple of linear equations and solving the equations. Question 1 A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many chickens were there in the farm? A. 70 B. 120 C. 60 D. 130 E. 80 The correct choice is (D) and the correct answer is 130. Explanatory Answer Let there by 'x' chickens and 'y' pigs. Therefore, x + y = 200 --- (1) Each chicken has 2 legs and each pig has 4 legs Therefore, 2x + 4y = 540 --- (2) Solving equations (1) and (2), we get x = 130 and y = 70. There were 130 chickens and 70 pigs in the farm.

Question 2: Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now? Question 2 Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now? A. 12 years B. 6 years C. 3 years D. 9 years E. 27 years The correct choice is (D) and the correct answer is 9 years. Explanatory Answer Let the age of the son 3 years back be x years Therefore, the age of the father 3 years back was x + 24 At present the age of the son is x + 3 and the father is 5 times as old as the son. i.e., x + 24 + 3 = 5(x + 3) i.e., x + 27 = 5x + 15 or 4x = 12 or x = 3. Therefore, the son was 3 years old 3 years back and he will be 9 years old three years from now. Question 3: For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution? The GMAT Sample Math question given below is from the topic Linear Equations and tests fundamental properties of a system of linear equations. Question 3 For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution? A. 12 B. 9 C. 3 D. 7.5 E. 2.5 The correct choice is (B) and the correct answer is 9. Explanatory Answer A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. That is, if they are not parallel lines. i.e., the two lines should have different slopes. ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if their slopes are different.

i.e., when In the question given above, a = 3, b = 4, d = k and e = 12.

Therefore,

or 'k' should not be equal 9 for the pair of equations to have a unique solution.

Question 1: If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?Question 1 If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x? A. 395 B. 275 C. 355 D. 415 E. 365 The correct choice is (A) and the correct answer is 395. Explanatory Answer The average (arithmetic mean) of the 5 numbers 28, x, 42, 78 and 104 is 62. Therefore, the sum of these 5 numbers is 62 * 5 = 310 i.e., 28 + x + 42 + 78 + 104 = 310 Hence, x = 310 - 252 = 58.

The average of 128, 255, 511, 1023 and x =

= 395

Question 2: The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2? Question 2