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If s and t are positive integers such that s/t = 64.12 which [#permalink]
 02 Jul 2012, 02:08
Question Stats:
64% (02:22) correct
35% (01:03) wrong based on 6 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectIf 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 Diagnostic Test
Question: 13
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 02:08
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SOLUTIONIf 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 divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3 Answer. E.
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 02:27
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Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectIf 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 Diagnostic Test
Question: 13
Page: 22
Difficulty: 650 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! We can rewrite the given equality as s = 64t + 0.12t. The divider is t, the quotient is 64. The remainder is 0.12t (it is less than t) and it is an integer, being equal to s-64t. Since 0.12t=\frac{3}{25} t, it follows that t should be a multiple of 25, so t=25n, for some positive integer n. Therefore, the remainder is 3n, or a multiple of 3. The only answer that is a multiple of 3 is 45. Answer: E
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 02:55
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i dont know if this method is correct or not, would need expert check
s/t = 64.12
= 64+12/100
= 64+3/25
i got 3, and in the options the multiple of is 45
Answer - E
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
02 Jul 2012, 03:11
Hi, Difficulty level: 600 s/t = 64.12 or s/t = 64 + 0.12 = 64 + 12/100 = 64 + 3/25; 3/25 will give the remainder. Thus, the reminder should be multiple of 3. Answer (E) Regards,
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
06 Jul 2012, 02:57
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SOLUTIONIf 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 divided by t yields the remainder of r can always be expressed as: \frac{s}{t}=q+\frac{r}{t} (which is the same as s=qt+r), where q is the quotient and r is the remainder.Given that \frac{s}{t}=64.12=64\frac{12}{100}=64\frac{3}{25}=64+\frac{3}{25}, so according to the above \frac{r}{t}=\frac{3}{25}, which means that r must be a multiple of 3. Only option E offers answer which is a multiple of 3 Answer. E.
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If s and t are positive integers such that s/t = 64.12 which [#permalink]
18 Aug 2012, 05:50
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Shortcut for this question:- 64.12 = 64 + 12/100 Now focus on remainder part which is 12/100= 3/25 Because 3 represents some fraction (ratio) of remainder , the remainder must be a multiple of 3. only 45 is a multiple of 3. Time taken app20sec Waiting for few kudos
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
18 Aug 2012, 10:00
+1 E 0.12 = 12/100 = 3/25, the remainder must be a multiple of 3.
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Divisibility / Remainder problem [#permalink]
28 Aug 2012, 02:08
Question is:
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
Is there a quick/definitive way of solving this without finding an expression for the remainder (i.e. 0.12 = remainder) and testing each answer choice from A-E?
Thanks,
elegan
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Re: Divisibility / Remainder problem [#permalink]
28 Aug 2012, 02:32
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, => s = t*64.12 => s = 64t + t*.12 So, when s is divided by t then we will get t*.12 as reminder (as t*.12 will be less than t) Now t is an integer and .12 is 12*.01 which means it is 3*something So, only answer choices which are multiple of 3 are contenders. Only possbility is E! Hope it helps!
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Re: Divisibility / Remainder problem [#permalink]
28 Aug 2012, 02:57
Answer is E
S/T = 64.12 or you can write it as 6412/100 or 1603/25
So, If we divide 1603 by 25 we will get remainder of 3.
From the five options, only 45 is divisible by 3 So, The answer should be 45.
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Re: Divisibility / Remainder problem [#permalink]
28 Aug 2012, 03:03
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Re: If s and t are positive integers such that s/t = 64.12 which [#permalink]
28 Aug 2012, 08:20
its E...
i think diffculty level is 650.. i knw we can do it in 20 sec..but very few ppl knw this trick to solve this question..
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If s and t are positive integers such that s/t = 64.12, which of [#permalink]
26 Dec 2012, 23:15
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\frac{S}{t} = 64 + .12
S = 64t + .12t
The remainder is equal to .12t.
R = .12t
R/.12 = t
We have to look for R where R/.12 is an integer.
A)2/.12 = 200/12 is not an integer
B)4/.12 = 400/12 = 100/3 is not an integer
C) 8/.12 = 800/12 = 400/6 = 200/3 is not an integer
D) also not
E) 45/12 = 4500/12 = 1500/4 = 15*25 is an integer
Answer: E
C)
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If s and t are positive integers such that s/t = 64.12, which of
[#permalink]
26 Dec 2012, 23:15
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