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# For the positive integers q, r, s, and t, the remainder when

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Manager
Joined: 06 Jun 2012
Posts: 82
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V38
For the positive integers q, r, s, and t, the remainder when [#permalink]

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21 Jul 2012, 13:38
3
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00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:39) correct 44% (01:52) wrong based on 306 sessions

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For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

A. 32
B. 38
C. 44
D. 52
E. 63

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Re: For the positive integers q, r, s, and t the remainder when [#permalink]

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21 Jul 2012, 14:09
2
6
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

1)32
2)38
3)44
4)52
5)63

Its obvious from the prompt that r is greater than 7 and t is greater than 3
so the product of rt must have at least 2 factors, one which is greater than 7 and other greater than 3
Now lets break down the possible factors so that this condition is validated
The (r,t) pairs for the options can be:
for 32, (8,4)
for 44, (11,4)
for 52 (13,4)
for 63 (9,7)
however 32 can only be written as 38*1 or 19*2 none of which can validate the prompt.
Hope this helps
Cheers
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Senior Manager
Joined: 22 Dec 2011
Posts: 271
For the positive integers q, r, s, and t, the remainder when [#permalink]

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24 Oct 2012, 22:57
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

A. 32
B. 38
C. 44
D. 52
E. 63

From the question we know that r >= 8 and s >=4

So A is possible, from there how to proceed?

Cheers
VP
Joined: 02 Jul 2012
Posts: 1192
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: For the positive integers q, r, s, and t, the remainder when [#permalink]

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24 Oct 2012, 23:24
1
Jp27 wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

32
38
44
52
63

OA

From the question we know that r >= 8 and s >=4

So A is possible, from there how to proceed?

Cheers

$$32 = 2^5$$
$$38 = 2^1 * 19^1$$
$$44 = 2^2 * 11^1$$
$$52 = 2^2 * 13^1$$
$$63 = 3^2 * 7^1$$
All options other than B can be represented as a product of two numbers one being greater than or equal to 4 and the other being greater than or equal to 8.

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Re: For the positive integers q, r, s, and t, the remainder when [#permalink]

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25 Oct 2012, 04:12
3
1
Jp27 wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

A. 32
B. 38
C. 44
D. 52
E. 63

From the question we know that r >= 8 and s >=4

So A is possible, from there how to proceed?

Cheers

Important property: remainder cannot be greater than the divisor.

Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.

Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:

32=8*4
44=11*4
52=13*4
63=9*7

However, 38=1*38 or 19*2, thus rt cannot equal to 38.

Hope it's clear.
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Re: For the positive integers q, r, s, and t, the remainder when [#permalink]

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23 Mar 2015, 02:49
souvik101990 wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

1)32
2)38
3)44
4)52
5)63

however 32 can only be written as 38*1 or 19*2 none of which can validate the prompt.
Hope this helps
Cheers

Hi souvik101990!
I think there is a typo in bolded part of statement. There should be 38 not 32. Yes?
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VP
Joined: 07 Dec 2014
Posts: 1034
For the positive integers q, r, s, and t, the remainder when [#permalink]

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29 Aug 2017, 19:06
TechWithNoExp wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

A. 32
B. 38
C. 44
D. 52
E. 63

r>7
t>3
rt factor can't be<4
38 has two sets of factors: 1*38*and 2*19
1 and 2 are both<4
B
For the positive integers q, r, s, and t, the remainder when   [#permalink] 29 Aug 2017, 19:06
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