A Heap of Stones can be Made up into Groups of 21. When Made up into GMAT Problem Solving

Question: A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45, there are 3 stones lift in each case. How many stones atleast can there be in the heap?

1. 2403
2. 3603
3. 4803
4. 6203
5. 7203

“A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45, there are 3 stones lift in each case. How many stones atleast can there be in the heap?”- 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.

Answer:

Approach Solution 1:

A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45, there are 3 stones left in each case. How many stones at least can there be in the heap?
The number of stones are in the form of = LCM (16, 20, 25, and 45) * k + 3 = 3600 * k + 3
Since the heap of stones can be made up of the groups of 21, the number of stones 3600 * k + 3 should be divisible by 21
Since the remainder when 3 divided by 21 is 3. 3600 * k should leave a remainder 18 when divided by 21

Remainder when 3600 divided by 21 = 9
9*k = 18
k = 2
Number of stones = 3600 * 2 + 3 = 7203

Correct option: E

Approach Solution 2:

Heap of stones can be made up into groups of 21, which means that the total number of stones in that heap must be divisible by 21 = 7 * 3
But it should not be divisible by 16 (4*4), 20 (4*5), 25 (5*5) and 45 (9*5)
Vertically scan through the options. Only option (e) is divisible by 7.

Correct option: E

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