What Is The Greatest Positive Four-Digit Integer Which Must Be Added GMAT Problem Solving

Question: What is the greatest positive four-digit integer which must be added to 5231 so that the final number becomes divisible by 12, 15, 27, 32 and 40?

  1. 9729
  2. 7929
  3. 7829
  4. 7729
  5. 6729

Approach Solution (1)

The smallest number that is divisible by 12, 15, 27, 32 and 40 is LCM, which turns out to be 4320.
4320 is less than 5231.
Therefore, we get 4320 * 2 = 8640
8640 - 5231 = 3409, which is not even in the answer choices because the question asks for the greatest positive four-digit integer.
So 3409 + 4320 = 7729

Correct option: D

Approach Solution (2)

12: 3∗4
15: 3∗5
27: 3^3
32: 2^5
40: 5∗2^3

LCM: 2^5 ∗ 3^3 ∗ 5
32 ∗ 27 ∗ 5 = 4320

The answer will be the choice which when added to 5231 yields a multiple of 4320
Looking at the sum of 5231 and each of the answer choices, their respective sums will range somewhere between 11000 and 16000
Multiples of 4320 which are 5 digits big will 4320 ∗ 3 and 4320 ∗ 4
However, 4320∗4 will take us out of the range of between 11000 and 16000.
Therefore, 4320 ∗ 3 = 12960

Correct option: D

Approach Solution (3)

5321 + 4 digit number which should be divisible by 12,15,27,32 , 40
TWe will take LCM
Therefore, we get 2^3*3^3*5 = 4320
5231+7729
12960 is divisible by 4320

Correct option: D

“What is the greatest positive four-digit integer which must be added to 5231 so that the final number becomes divisible by 12, 15, 27, 32 and 40?”- 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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