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For the positive integers q, r, s, and t, the remainder when
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21 Jul 2012, 13:38

4

30

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

58% (02:19) correct 42% (02:30) wrong based on 357 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:

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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25 Oct 2012, 04:12

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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

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

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

So, answer should be B

Kudos Please... If my post helped.
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For the positive integers q, r, s, and t, the remainder when
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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

Re: For the positive integers q, r, s, and t, the remainder when
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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. Hence answer is B 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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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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28 Aug 2018, 13:55

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.