GRE : Sample Questions with Solution

A: The quantity in Column A is greater.
B: The quantity in Column B is greater.
C: The two quantities are equal.
D: The relationship cannot be determined from the information given.

1. Column A                                                                                                                     Column B

    15² + 17² + 19²                                                                                                        (15 + 17 + 19)²

We know that the square of a sum of n positive numbers is always greater than the sum of the squares of the n numbers. For example, 25 = (2 + 3)² > 2² + 3² = 13. So, (15 + 17 + 19)² is greater than 15² + 17² + 19².

Hence, Column B is greater than Column A, and the answer is (B).

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2. Column A                                     The average temperature in New                           Column B

                                                           Orland from January through

                                                            August is 36°C. The minimum

                                                            and the maximum temperatures

                                                            between September and December

                                                            are 26°C and 36°C, respectively.

The average temperature for the                                                                                        36°C

Year

We are given that the average temperature from January through August is 36°C.

The average of a set of numbers always lies between the smallest number and the greatest number in the set. The minimum and the maximum temperatures between September and December are 26°C and 36°C, respectively. Hence, the average temperature of the period lies between 26°C and 36°C. So, the average temperature for the period September through December is less than 36°C.

So, the overall temperature for the year is less than 36°C. Hence, Column A is less than Column B, and the answer is (B).

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3.Column A                                        Park, Jack, and Galvin distributed                  Column B

                                                              prize money of 120 dollars among

                                                              themselves. Park received 3/10 of

                                                              what Jack and Galvin together

                                                              received. Jack received 3/11 of

                                                              what Park and Galvin together

                                                              received.

The amount received by Park                                                                   The amount received by Jack

Let the amounts received by Park, Jack, and Galvin be P, J, and G, respectively.

Since the prize money of $120 was distributed to Park, Jack, and Galvin, the amount that Jack and Galvin together received equals 120 – (the amount received by Park) = 120 – P.

Since we are given that Park received 3/10 of what Jack and Galvin together received, we have the equation

P = (3/10)(120 – P)

P = 3/10 ⋅ 120 – 3/10 ⋅ P

P + 3/10 ⋅ P = 3/10 ⋅ 120

13/10 ⋅ P = 3/10 ⋅ 120

P = 3/13 ⋅ 120 = Column A

Similarly, since we are given that Jack received 3/11 of what Park and Galvin together received (120 – J),

we have the equation

J = (3/11)(120 – J)

J = 3/11 ⋅ 120 – 3/11 ⋅ J

J + 3/11 ⋅ J = 3/11 ⋅ 120

14/11 ⋅ J = 3/11 ⋅ 120

J = 3/14 ⋅ 120 = Column B

Since 3/13 ⋅ 120 is greater than 3/14 ⋅ 120, Column A > Column B and the answer is (A).

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4.Column A                                 Jack, Karl, Marc, and Kate are                        Column B

                                                      friends. They collected just

                                                      enough money to buy a car. Jack

                                                      contributed 1/3 of what his three

                                                      friends contributed together. Karl

                                                      contributed 1/4 of what his three

                                                      friends contributed together. Marc

                                                      contributed 2/5 of what his three

                                                      friends contributed together.

The amount paid by Jack                                                                                The amount paid by Marc

Marc contributed 2/5 of what his three friends contributed together, while Jack contributed only 1/3 of what his three friends contributed together. Clearly, Marc must have contributed more than Jack. Let’s see this in detail:

Let the total contribution of the four friends be T, the contribution by Jack be J, and the contribution by Marc be M.

Now, the contribution by the three friends other than Jack is T – J. Jack contributed 1/3 of this. Hence, we have J = (1/3)(T – J), or J = T/4 (by solving for J).

Also, the contribution by the three friends other than Marc is T – M. As given, Marc contributed 2/5 of this.

Hence, we have M = (2/5)(T – M), or M = 2T/7 (by solving for M).

Now, 2T/7 is greater than T/4 and therefore Marc contributed more. The answer is (B).

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5. Column A                                             720 cents can buy 72 bananas.                    Column B

                                                                     If the price of each banana is

                                                                     reduced by 1 cent, 720 cents can

                                                                      buy 72 + x bananas.

                                                                      If the price of each banana is

                                                                      reduced by 2 cents, 720 cents can

                                                                     buy 72 + y bananas.

    2 x                                                                                                                                                   y

Since 72 bananas cost 720 cents, each banana costs 720/72 = 10 cents.

When price is reduced by 1, the new price is 10 – 1 = 9 cents. Hence, 720 cents can buy 80 (= 720/9) bananas. Equating this to 72 + x yields 72 + x = 80, or x = 80 – 72 = 8.

When price is reduced by 2, the new price is 10 – 2 = 8 cents. Hence, 720 cents can buy 90 (= 720/8) bananas. Equating this to 72 + y yields 72 + y = 90, or y = 90 – 72 = 18.

Now, Column A equals 2x = 2(8) = 16, and this is less than 18 (= Column B). The answer is (B).

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GRE : Sample Questions with Solution

1. In how many ways can the letters of the word MAXIMA be arranged such that all vowels are

together?

(A) 12

(B) 18

(C) 30

(D) 36

(E) 72

The base set can be formed as {{A, I, A}, M, X, M}. The unit {A, I, A} arranges itself in 3P3/2!

ways. The 4 units in the base set can be arranged in 4P4/2! ways. Hence, the total number of ways of arranging the letters is 3P3/2! . 4 P4/2!

=3!/2!  . 4!/2!

= 3.12 = 36

The answer is (D).

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2. If x + z > y + z, then which of the following must be true?

(I) x – z > y – z

(II) xz > yz

(III) x/z > y/z

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) II and III only

 Canceling z from both sides of the inequality x + z > y + z yields x > y. Adding –z to both sides yields x –z > y – z. Hence, I is true.

If z is negative, multiplying the inequality x > y by z would flip the direction of the inequality resulting in the inequality xz < yz. Hence, II may not be true.

If z is negative, dividing the inequality x > y by z would flip the direction of the inequality resulting in the inequality x/z < y/z. Hence, III may not be true.

The answer is (A) since we are asked for statements that MUST be true.

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3. If yz – zx = 3 and zx – xy = 4, then xy – yz =

(A) –7

(B) 1

(C) 3

(D) 4

(E) 7

 Adding the two given equations yields

(yz – zx) + (zx – xy) = 3 + 4

yz – zx + zx – xy = 7

yz – xy = 7

xy – yz = –7 multiplying both sides by –1

The answer is (A).

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4. The cost of production of a certain instrument is directly proportional to the number of units produced. The cost of production for 300 units is $300. What is the cost of production for 270 units?

(A) 270

(B) 300

(C) 325

(D) 370

(E) 395

   The cost of production is proportional to the number of units produced. Hence, we have the equation The Cost of Production = k × Quantity, where k is a constant.

We are given that 300 units cost 300 dollars. Putting this in the proportionality equation yields 300 = k × 300. Solving the equation for k yields k = 300/300 = 1. Hence, the Cost of Production of 270 units equals k × 270 = 1 × 270 = 270. The answer is (A).

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5. The list price of a commodity is the price after a 20% discount on the retail price. The festival discount price on the commodity is the price after a 30% discount on the list price. Customers purchase commodities from stores at a festival discount price. What is the effective discount offered by the stores on the commodity on its retail price?

(A) 20%

(B) 30%

(C) 44%

(D) 50%

(E) 56%

 

 Let r be the retail price. The list price is the price after a 20% discount on the retail price. Hence, it equals r(1 – 20/100) = r(1 – 0.2) = 0.8r.

The festival discount price is the price after a 30% discount on the list price. Hence, the festival discount price equals (list price)(1 – 30/100) = (0.8r)(1 – 30/100) = (0.8r)(1 – 0.3) = (0.8r)(0.7) = 0.56r. Hence, the total discount offered is (Original Price – Price after discount)/Original Price × 100 =(r – 0.56r)/ r × 100 = 0.44 × 100 = 44%.

The answer is (C).

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