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

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

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New post Updated on: 23 Nov 2013, 06:02
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-positive-integers-q-r-s-and-t-the-remainder-when-141251.html

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Originally posted by krishnasty on 09 Oct 2011, 07:27.
Last edited by Bunuel on 23 Nov 2013, 06:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: positive integers q, r, s, and t  [#permalink]

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New post 09 Oct 2011, 08:28
4
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"
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Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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New post 23 Nov 2013, 06:03
4
5
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.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-positive-integers-q-r-s-and-t-the-remainder-when-141251.html
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Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

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New post 21 Sep 2018, 04:28
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Re: For the positive integers q, r, s, and t, the remainder when &nbs [#permalink] 21 Sep 2018, 04:28
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