Question: 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?

1. 328
2. 348
3. 258
4. 358
5. 400

Answer:
Approach Solution (1):
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:

1. 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

2. 348

348 is 8 greater than 340, and 340 is not a multiple of 25.
Eliminate B

100. 258

258 is 8 greater than 250, and 250 is a multiple of 25
Keep C

500. 358

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

5. 400

400 is 8 greater than 392, and 392 is a multiple of 25.
Eliminate E
We’re left with C and D
Had the number of children been 28, 22 sweets have been left after equally distributing
In other words, the number of treats is 22 greater than some multiple of 28

100. 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
By the process of elimination, we get the correct answer: D

Correct option: D
Approach Solution (2):
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 * 14 + 8) = 358

Correct option: D
Approach Solution (3):
25x + 8 = 28y + 22
25x = 28y + 22 – 8
25x = 28y + 14
25x = (2y + 1) * 14
So, 2y + 1 = 25 and y = 14
2y = 25 – 1 = 24
y = 12 (Substitute here 28y + 22)
So, we will get:
28 (12) + 22 = 358

Correct option: D

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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