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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

Kudos [?]: 37 [3], given: 9

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

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21 Jul 2012, 13:38
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Difficulty:

65% (hard)

Question Stats:

56% (01:40) correct 44% (01:49) wrong based on 279 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
[Reveal] Spoiler: OA

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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
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Expert's post
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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:

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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Kudos [?]: 16205 [1], given: 1952

Senior Manager
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Kudos [?]: 282 [0], given: 32

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

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24 Oct 2012, 22:57
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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

[Reveal] Spoiler:
From the question we know that r >= 8 and s >=4

So A is possible, from there how to proceed?

Cheers

Kudos [?]: 282 [0], given: 32

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

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24 Oct 2012, 23:24
1
KUDOS
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
[Reveal] Spoiler:
B

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.

Kudos Please... If my post helped.
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Kudos [?]: 1621 [1], given: 116

Math Expert
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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
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Expert's post
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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

[Reveal] Spoiler:
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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21 Jul 2014, 19:44
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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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Kudos [?]: 87 [0], given: 349

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

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17 Aug 2016, 23:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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25 Aug 2017, 08:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

Kudos [?]: 223 [0], given: 10

For the positive integers q, r, s, and t, the remainder when   [#permalink] 29 Aug 2017, 19:06
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