If X + Y = 7, Y + Z = 5, and Z + W = 8, then… | GMAT Sprint

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PS · Problem Solving

555-605

Algebra

If X + Y = 7, Y + Z = 5, and Z + W = 8, then XY + WZ + XZ + YW is:

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Explanation

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Official Explanation

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To solve for XY + WZ + XZ + YW, we first need to express each variable in terms of one variable. From the equations, we have: 1) X + Y = 7, so Y = 7 - X. 2) Y + Z = 5, substituting Y gives us (7 - X) + Z = 5, which simplifies to Z = X - 2. 3) Z + W = 8, substituting Z gives us (X - 2) + W = 8, which simplifies to W = 10 - X. Now we can express XY, WZ, XZ, and YW: XY =…

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Comments

ashrithApr 14, 2025

Amazing

SritamApr 26, 2025

Thanks for sharingThank you for sharing!!thanks for sharing

WaheedJan 11, 2025

thanks for taking time to upload it!

TarekMar 17, 2025

finally understood this

JustinMay 4, 2024

thanks

ChrisJul 6

Wait, the credited answer is 50? That seems way bigger than the answer choices I'd expect. Can someone explain how it works out to that?

GarimaJul 20

yeah it surprised me too. if you group the expression differently you'll notice some of the terms pair up in a way that isn't obvious at first

AshitaJul 19

same, I had 20 circled and then saw the answer. grouping is key here

ShayneJul 8

Is there a way to solve this without finding X, Y, Z, and W individually? Feels like a lot of work for a 4-variable system with only 3 equations.

PradeepJul 17

yes! you don't need individual values. try factoring XY + WZ + XZ + YW by grouping the X terms and the W terms. the given sums fall out nicely

RitvikJul 13

this. once you see the grouping it's like 20 seconds of work

AdityaSep 28

tricky one. the grouping is clever but I kept trying to solve for each variable first and got nowhere. good reminder to look at the target expression before diving in

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.