If a is 4041 of 4142 and b = 4041, then ab = | GMAT Sprint

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PS · Problem Solving

sub-505

Arithmetic

If a is $\frac{40}{41}$ of $\frac{41}{42}$ and b = $\frac{40}{41}$ , then $\frac{a}{b} =$

Answer Choices

Correct answer marked below

\frac{1600}{1682}

\frac{40}{42}

\frac{40}{41}

\frac{41}{42}

Correct

\frac{1682}{1600}

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Explanation

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Official Explanation

Official

To find

a

, we calculate

a = \frac{40}{41} \times \frac{41}{42} = \frac{40}{42}

. Since [m]b =…

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Comments

AkshayaFeb 10, 2025

Great

HARDIKOct 8, 2024

Greatt

HunterOct 4, 2024

Can someone explain it other way?

JacobJun 10

Easy one. a is just b times 41/42, so a/b is 41/42. Took like 10 seconds.

AnhJun 18

yep same, the b cancels right out

JaceMay 10

wait the 40/41 looks scary at first but it basically cancels. nice

SanyuktaMay 5

i overthought this and started multiplying fractions lol. then realized a is just b times 41/42

LoaiMay 7

same haha, the long multiplication is such a trap

GuluMay 10

isn't the trick just that a/b makes the 40/41 disappear?

What this question tests

What it tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Common trap

Applying the order of operations out of sequence or rounding intermediate values before the final step.

If a is 4041\frac{40}{41}4140​ of 4142\frac{41}{42}4241​ and b = 4041\frac{40}{41}4140​, then ab=\frac{a}{b} =ba​=