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What is the smallest positive integer which when increased by 3 is div
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05 Aug 2021, 06:00
05 Aug 2021, 06:00
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Difficulty:
15%
(low)
Question Stats:
82% (01:29) correct
18%
(01:44)
wrong
based on 66
sessions
What is the smallest positive integer which when increased by 3 is divisible by 16, 24, 30 and 32?
(A) 480
(B) 477
(C) 475
(D) 472
(E) 471
(A) 480
(B) 477
(C) 475
(D) 472
(E) 471
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Joined: 12 Jun 2018
Posts: 10
Given Kudos: 11
Location: India
Schools: ISB '24 (A)
GMAT 1: 710 Q48 V39
GPA: 4
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Re: What is the smallest positive integer which when increased by 3 is div
[#permalink]
14 Aug 2022, 16:49
14 Aug 2022, 16:49
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The options make the question quite easy.
Note that the resultant (x+3) should be divisible by 30. The only option which has a 7 in the units place and would end in 0 on adding 3 is 477.
Posted from my mobile device
Note that the resultant (x+3) should be divisible by 30. The only option which has a 7 in the units place and would end in 0 on adding 3 is 477.
Posted from my mobile device
Re: What is the smallest positive integer which when increased by 3 is div
[#permalink]
05 Aug 2021, 06:10
05 Aug 2021, 06:10
The smallest positive integer divisible by 16, 24, 30, and 32 would be the LCM of these four numbers
=> 16 = 2^4
=> 24 = 2^3 * 3
=> 30 = 2 * 3 * 5
=> 32 = 2^5
LCM = 2^5 * 3 * 5 = 480
The number that we are looking for is = 480 - 3 = 477
OA should be B
=> 16 = 2^4
=> 24 = 2^3 * 3
=> 30 = 2 * 3 * 5
=> 32 = 2^5
LCM = 2^5 * 3 * 5 = 480
The number that we are looking for is = 480 - 3 = 477
OA should be B
