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Woody19
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After distributing the sweets equally among 25 children, 8 sweets rem Updated on: 07 Jul 2019, 06:45
Originally posted by Woody19 on 07 Jul 2019, 06:11.
Last edited by Woody19 on 07 Jul 2019, 06:45, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

73% (02:42) correct 27% (02:44) wrong based on 304 sessions

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After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28 , 22 sweets would have been left after equally distributing. Which is the following COULD be the total number of sweets??

A. 328

B. 348

C. 258

D. 358

E. 400
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D
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BrentGMATPrepNow
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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 06:55
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Woody19
After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28 , 22 sweets would have been left after equally distributing. Which is the following COULD be the total number of sweets??

A. 328

B. 348

C. 258

D. 358

E. 400
Show more

The approach I'd take on test day is to test the answer choices

After distributing the sweets equally among 25 children, 8 sweets remain
If the number of treats were a multiple of 25, then there would be ZERO sweets remaining.
So, we know that the number of treats is 8 greater than some multiple of 25

Now check the answer choices....
A. 328
Is 328 8 greater than some multiple of 25?
No. 328 is 8 greater than 320, and 320 is NOT a multiple of 25
ELIMINATE A.

B. 348
348 is 8 greater than 340, and 340 is NOT a multiple of 25. ELIMINATE B

C. 258
258 is 8 greater than 250, and 250 IS a multiple of 25. KEEP C

D. 358
358 is 8 greater than 350, and 350 IS a multiple of 25. KEEP D

E. 400
400 is 8 greater than 392, and 392 is NOT a multiple of 25. ELIMINATE E

We're left with C and D

Had the number of children been 28 , 22 sweets would have been left after equally distributing.
In other words, the number of treats is 22 greater than some multiple of 28

C. 258
Is 258 22 greater than some multiple of 28?
No. 258 is 22 greater than 236, and 236 is NOT a multiple of 28
ELIMINATE C

By the process of elimination, the correct answer is D

Cheers,
Brent
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After distributing the sweets equally among 25 children, 8 sweets rem 10 Jul 2019, 04:26
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prabsahi
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This question should be worded as "Which is the following COULD be the total number of sweets?", because there's more than one correct answer to the original question.
For example, the answer COULD be 358 (D) or it COULD be 1058, or it COULD be 1758, etc


Hello Brent considering the scope of options is less than 400.I guess I will go for 358.

I was trying it this way.

t= 25x + 8
t= 28y + 22

where x ad y are integers and t is total number of sweets.(More like a reaminder problem)

Now
25x + 8 = 28y + 22

25x - 28y = 16

After this I got struck. Can you please help me with the above approach.


Another approach
t= 25x + 8 ,t= 28y + 22
based on this I will basically try to divide each option by 25 and see when we are left with 8 and similarly later on divide by 28 and see when we have 22 as remainder.
and this approach you have already provided a beautiful explanation.
Show more


hello prabsahi

\(25x + 8= 28y + 22\)

\(25x = 28y+14\)

\(25x = (2y+1)*14\) so \(2y+1 = 25\) and \(y =14\)

\(2y+1 = 25\)

\(2y =24\)

\(y = 12\) (substitute here \(28y + 22\))

\(28(12) +22 = 358\)

hope it helps :)
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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 06:43
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This question should be worded as "Which is the following COULD be the total number of sweets?", because there's more than one correct answer to the original question.
For example, the answer COULD be 358 (D) or it COULD be 1058, or it COULD be 1758, etc
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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 06:46
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Thanks GMATPrepNow :)

Kindly provide the solution.
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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 06:59
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The answer must be a multiple of 25 plus 8, so you can eliminate A, B and E. The remainder of 258/22 is 14, not 22, so the answer is 358.

Ans. D

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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 07:04
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GMATPrepNow
This question should be worded as "Which is the following COULD be the total number of sweets?", because there's more than one correct answer to the original question.
For example, the answer COULD be 358 (D) or it COULD be 1058, or it COULD be 1758, etc
Show more


Hello Brent considering the scope of options is less than 400.I guess I will go for 358.

I was trying it this way.

t= 25x + 8
t= 28y + 22

where x ad y are integers and t is total number of sweets.(More like a reaminder problem)

Now
25x + 8 = 28y + 22

25x - 28y = 16

After this I got struck. Can you please help me with the above approach.


Another approach
t= 25x + 8 ,t= 28y + 22
based on this I will basically try to divide each option by 25 and see when we are left with 8 and similarly later on divide by 28 and see when we have 22 as remainder.
and this approach you have already provided a beautiful explanation.
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After distributing the sweets equally among 25 children, 8 sweets rem 07 Jul 2019, 07:21
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GMATPrepNow

Thanks a lot for the solution. Testing numbers takes less time.

Below is the solution given in the book.

Let the total number of sweets be 25x+8.
then 25x+8-22 is divisible by 28. => 25x-14 is divisible by 28
28x - ( 3x + 14 ) is divisible by 28 ---- NO IDEA how this equation is made.
(3x + 14 ) is divisible by 28 => x = 14 ---- NO IDEA about this as well.

Then total = ( 25 x 14 + 8 ) = 358.

Please explain highlighted part.

sorry for the silly question.
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After distributing the sweets equally among 25 children, 8 sweets rem 10 Jul 2019, 04:31
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Woody19
GMATPrepNow

Thanks a lot for the solution. Testing numbers takes less time.

Below is the solution given in the book.

Let the total number of sweets be 25x+8.
then 25x+8-22 is divisible by 28. => 25x-14 is divisible by 28
28x - ( 3x + 14 ) is divisible by 28 ---- NO IDEA how this equation is made.
(3x + 14 ) is divisible by 28 => x = 14 ---- NO IDEA about this as well.

Then total = ( 25 x 14 + 8 ) = 358.

Please explain highlighted part.

sorry for the silly question.
Show more


hi Woody19

if you subtract (28x+22) - (25x+8) you get = 3x+14

So to make 3x+14 divisible by 28 , x = 14 i.e. 3(14) +14 = 56 /28

so 25*14+8 = 358

have a great day :)
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After distributing the sweets equally among 25 children, 8 sweets rem 10 Jul 2019, 05:29
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dave13

I liked the solution that you provided to prabsahi

I can relate that approach to other problems as well.

Thank you. +1
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