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For the positive integers q, r, s, and t, the remainder when
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Updated on: 23 Sep 2019, 05:45

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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

Re: For the positive integers q, r, s, and t, the remainder when
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21 Jul 2012, 14:09

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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. Hence answer is B Hope this helps Cheers
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Re: For the positive integers q, r, s, and t, the remainder when
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09 Oct 2011, 08:28

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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

For the positive integers q, r, s, and t, the remainder when
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23 Nov 2013, 06:03

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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.

Re: For the positive integers q, r, s, and t, the remainder when
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24 Oct 2012, 23:24

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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

\(32 = 2^5\) \(38 = 2^1 * 19^1\) \(44 = 2^2 * 11^1\) \(52 = 2^2 * 13^1\) \(63 = 3^2 * 7^1\) 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.

Re: For the positive integers q, r, s, and t, the remainder when
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28 Aug 2018, 13:55

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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

Now check the answer choices...

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.

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

Re: For the positive integers q, r, s, and t, the remainder when
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23 Sep 2019, 05:44

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