bySayantani Barman Experta en el extranjero
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?
- 328
- 348
- 258
- 358
- 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:
- 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
- 348
348 is 8 greater than 340, and 340 is not a multiple of 25.
Eliminate B
- 258
258 is 8 greater than 250, and 250 is a multiple of 25
Keep C
- 358
358 is 8 greater than 350, and 350 is a multiple of 25.
Keep D
- 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
- 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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