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

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Difficulty:   75% (hard)

Question Stats: 56% (02:18) correct 44% (02:29) wrong based on 287 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

Originally posted by krishnasty on 09 Oct 2011, 07:27.
Last edited by Bunuel on 23 Sep 2019, 05:45, edited 2 times in total.
Renamed the topic and edited the question.
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Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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3
9
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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Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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1
krishnasty 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

r>=8 And t>=4

32=8*4(Possible)
38=19*2 OR 38*1, none of which is possible because 2 AND 1 are both less than 4 OR 8.
44=11*4
52=13*4
63=9*7

Ans: "B"
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59712
For the positive integers q, r, s, and t, the remainder when  [#permalink]

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4
7
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

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.

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

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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.

Kudos Please... If my post helped.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4145
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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Top Contributor
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

Great question!!

USEFUL PROPERTY:
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Conversely, if I know that, when k is divided by w, the remainder is 5, then I know that w must be greater than 5

The remainder when q is divided by r is 7
This tells us that r is greater than 7

s is divided by t is 3
This tells us that t is greater than 3

A) 32
Is it POSSIBLE for rt to equal 32?
Yes, if r = 8 and t = 4, then rt = 32
ELIMINATE A

B) 38
Is it POSSIBLE for rt to equal 38?
NO.
There are only two ways to write 38 as the product of POSITIVE INTEGERS:
i) (2)(19) = 38
ii) (1)(38) = 38
If r is greater than 7 and t is greater than 3, there's no way that one of the values (r or t) can equal 1 or 2.

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

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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
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Posts: 13742
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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_________________ Re: For the positive integers q, r, s, and t, the remainder when   [#permalink] 23 Sep 2019, 05:44
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