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

Question

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

souvik101990 · Accepted Answer

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

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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.

Answer: B

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

fluke · Answer

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"

MacFauz · Answer

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.

gracie · Answer

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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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

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