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For the positive integers q, r, s, and t, the remainder when q is divi
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14 Jul 2021, 05:15
14 Jul 2021, 05:15
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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
A. 32
B. 38
C. 44
D. 52
E. 63
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Re: For the positive integers q, r, s, and t, the remainder when q is divi
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14 Jul 2021, 05:28
14 Jul 2021, 05:28
2
Carcass 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
A. 32
B. 38
C. 44
D. 52
E. 63
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.
Answer: B
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Re: For the positive integers q, r, s, and t, the remainder when q is divi
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25 Sep 2022, 03:40
25 Sep 2022, 03:40
1
The remainder when q is divided by r is 7 and the remainder when s is divided by t is 3 and we need to find all of the following are possible values for the product rt EXCEPT
Theory: A number, when divided by a number k, can give remainder from 0 to k-1
The remainder when q is divided by r is 7
=> r > 7
=> Possible values of r are 8, 9 , 10, 11,...
The remainder when s is divided by t is 3
=> t > 3
=> Possible values of t are 3, 4, 5, 6,...
Let's see which all options we can make for rt
A. 32
r = 8, t = 4 => rt = 32 => POSSIBLE
B. 38
r = 19, t = 2 => rt = 38 But t cannot be 2 => NOT POSSIBLE
In test, we don't need to solve further but I am solving to complete the solution.
C. 44
r = 11, t = 4 => rt = 44 => POSSIBLE
D. 52
r = 13, t = 4 => rt = 52 => POSSIBLE
E. 63
r = 9, t = 7 => rt = 63 => POSSIBLE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: A number, when divided by a number k, can give remainder from 0 to k-1
The remainder when q is divided by r is 7
=> r > 7
=> Possible values of r are 8, 9 , 10, 11,...
The remainder when s is divided by t is 3
=> t > 3
=> Possible values of t are 3, 4, 5, 6,...
Let's see which all options we can make for rt
A. 32
r = 8, t = 4 => rt = 32 => POSSIBLE
B. 38
r = 19, t = 2 => rt = 38 But t cannot be 2 => NOT POSSIBLE
In test, we don't need to solve further but I am solving to complete the solution.
C. 44
r = 11, t = 4 => rt = 44 => POSSIBLE
D. 52
r = 13, t = 4 => rt = 52 => POSSIBLE
E. 63
r = 9, t = 7 => rt = 63 => POSSIBLE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
