If P is the product of integers from 150 to 3… | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

If P is the product of integers from 150 to 350 inclusive, and if Q is the product of integers 150 to 351, inclusive, what is $\frac{1}{P} + \frac{1}{Q}$ in terms of Q?

Answer Choices

Correct answer marked below

\frac{3512}{Q}

\frac{(352Q)}{351}

352Q

\frac{352}{Q}

Correct

(352)(351)Q^2

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Explanation

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Official Explanation

Official

To solve for

\frac{1}{P} + \frac{1}{Q}

, we first express

P

and

Q

. We have

P = 150 \times 151 \times \ldots \times 350

and

Q = 150 \times 151 \times \ldots \times 351

. Notice that

Q = P \times 351

. Therefore, we can rewrite

\frac{1}{P} + \frac{1}{Q}

as follows:

\frac{1}{P} + \frac{1}{Q} = \frac{1}{P} + \frac{1}{P \times 351} = \frac{1}{P} + \frac{1}{351P} = \frac{351 + 1}{351P} = \frac{352}{351P}

.…

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Comments

CarolinaFeb 22, 2025

Great question!

2020MEB098Jan 18, 2025

thank you for sharing

ShimantaMar 29, 2025

still struggling with these types of problems

ThitiratMar 6, 2024

Love how you solved this

PriteshJan 8, 2025

thank you for sharing

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

If P is the product of integers from 150 to 350 inclusive, and if Q is the product of integers 150 to 351, inclusive, what is 1P+1Q\frac{1}{P} + \frac{1}{Q}P1​+Q1​ in terms of Q?