integer divisibility

neha shekhawat wrote:If s and t are positive integers such that s/t=64.12,which of the following could be the remainder when s is divided by t?
A) 2
B) 4
C) 8
D) 20
E) 45

Let's examine a few things about remainders and decimal conversions.
7/4 = 1 3/4 = 1.75. When we divide 7 by 4, the remainder is 3, and .75 = 3/4.
32/5 = 6 2/5 = 6.4. When we divide 32 by 5, the remainder is 2, and .4 = 2/5.
58/20 = 2 18/20 = 2.9. When we divide 58 by 20, the remainder is 18, and .9 = 18/20.
As you can see, there is an important relationship between the remainder and the decimal part of the conversion.

64.12 = 64 12/100 = 6412/100. So, it's possible that s/t = 6412/100, in which case the remainder is 12 when s is divided by t.
Check the answer choices. . . nope, 12 is not one of the options.

Also, recognize that 64.12 = 64 12/100 = 64 3/25 = 1603/25. So, it's possible that s/t = 1603/25, in which case the remainder is 3 when s is divided by t.
Check the answer choices. . . nope, 3 is not one of the options.

At this point, we should recognize that we can get ANY MULTIPLE OF 3 as the remainder.
For example, 64.12 = 64 12/100
= 64 3/25
= 64 6/50
= 3206/50 = s/t, in which case the remainder is 6 when s is divided by t.

Or...64.12 = 64 12/100
= 64 3/25
= 64 9/75
= 4809/75 = s/t, in which case the remainder is 9 when s is divided by t.

And so on.

Since only one answer choice (E) is A MULTIPLE OF 3, E must be the correct answer.

Aside: Here's further proof:
64.12 = 64 12/100
= 64 3/25
= 64 45/375
= 24045/375 = s/t, in which case the remainder is 45 when s is divided by t.

Cheers,
Brent

neha shekhawat wrote:Thanks for detailed explanation.Can u please tell me the difficulty level of this question.

I'd say it's in the 550 to 600 range.

Cheers,
Brent

neha shekhawat wrote:If s and t are positive integers such that s/t=64.12, which of the following could be the remainder when s is divided by t?
A) 2
B) 4
C) 8
D) 20
E) 45

s/t=64.12 = 64 + 0.12

The remainder 0.12 = 12/100. The reduced form of 12/100 = 3/25. The reminder can be anything that is a multiple of '3'.

The correct answer: E

Relevant book: Manhattan Review GMAT Number Properties Guide

Hope this helps!

-Jay
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Matt@VeritasPrep wrote:
On the modern GMAT, maybe, since the math has gotten quite a bit more difficult than it used to be. But for the typical student I see in my classes (North American, college educated, but with minimal math practice in the last five to ten years of their lives) this not an easy one at all, so readers, don't feel bad if you struggled with it.

601?

Agreed, it's not easy.

In fact, my first inclinations was to peg it around 650+.
However, I noticed that it's question #95 (out of 230 Problem Solving questions) in the OG2015.
Since the OG2015 has its questions listed in order of difficulty, I downgraded my guess

Cheers,
Brent