(Q 358) GMAT / GRE Word Problem

A rectangular shed has a perimeter of 40 meters and a diagonal length of 15 meters. What is the area of the shed in square meters?

(A) 120

(B) 106.5

(C) 93.5

(D) 87.5

(E) 80

Let's say the width of the shed is W and the length is L. Then we know that

2W + 2L = 40, or W + L = 20 and

W² + L² = 15² = 225.

If we square both sides of the first equation, we get

(W+L)² = 400

W² + L² + 2WL = 400.

Since we know that W² + L² = 225, we can simplify the equation to

225 + 2WL = 400

2WL = 175

WL = 87.5

The quantity WL is the area of the shed, since the area of a rectangle is width times length. So the correct answer is D.

(Q 357) GMAT Data Sufficiency

Let A, B, C, and D be digits 0-9. If AB and CD represent two 2-digit numbers, is (AB)(CD) odd?

(1) A + C = 9

(2) B + D = 9

The product of two numbers is odd only when both numbers are odd. And since even/odd depends only on the last digit of a number, this means that (AB)(CD) will be odd only when (B)(D) is odd.

Statement 1 is insufficient because it gives us no information about B or D.

Statement 2 is sufficient to answer the question. This tells us that either B is even and D is odd, or B is odd and D is even. So (B)(D) must be even, therefore the answer to the question is "no."

The correct answer is B.

(Q 356) GMAT / GRE Factoring

a and b are positive integers and [(a^1/4)(b^1/3)]¹² = 2000. What is a+b?

(A) 200

(B) 108

(C) 50

(D) 12

(E) 7

The expression [(a^1/4)(b^1/3)]¹² can be rewritten as [(a³)(b⁴)]. To determine the values of a and b, we should start by factoring 2000 into its prime factors.

Notice that 2000 = (10)(10)(10)(2) = 2 x 5 x 2 x 5 x 2 x 5 x 2, or 2⁴5³. So the only possible solution is a=5 and b=2. Therefore a+b = 7 and the correct answer is E.

(Q 355) GMAT / GRE Algebra

Suppose a, b, and c are positive numbers, and a/b = 4, b/c = 3. What is (a+2b+3c)/(a+b+c)?

(A) 21/16
(B) 19/16

(C) 17/12
(D) 17/8
(E) 11/8

We can replace a and b with expressions in terms of c. Since b/c = 3, we have b = 3c. And since a/b = 4, we have a/(3c) = 4, or a = 12c. Then the fraction becomes

(12c + 6c + 3c)/(12c + 3c + c) = (21c)/(16c) = 21/16.

So the correct answer is A.

(Q 354) GMAT / GRE Exponents

What is the largest integer x such that 3^7x5^4x divides evenly into 45⁴⁷?

(A) 12
(B) 11
(C) 10
(D) 8
(E) 7

Note that 45⁴⁷ = (3²5)⁴⁷ = 3⁹⁴5⁴⁷.

3^7x5^4x will divide evenly into 3⁹⁴5⁴⁷ so long as 7x ≤ 94 and 4x ≤ 47.

Since 94/7 = 13.### and 47/4 = 11.###, the largest allowable value for x is 11.