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What is the least positive integer which is a multiple of 31 and when

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Bunuel
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What is the least positive integer which is a multiple of 31 and when [#permalink] New post   05 Aug 2021, 07:00
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What is the least positive integer which is a multiple of 31 and when divided by 15, 24 and 32 leaves the remainders 2, 11 and 19, respectively ?

(A) 2418
(B) 2387
(C) 2356
(D) 2325
(E) 2125
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B
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abuc0112
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Re: What is the least positive integer which is a multiple of 31 and when [#permalink] New post   05 Aug 2021, 07:15
My attempt

After subtracting the remainder 2 from each answer, the only one divisible by 15 is 2387

Answer is C
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Re: What is the least positive integer which is a multiple of 31 and when [#permalink] New post   05 Aug 2021, 09:10
Bunuel wrote:
What is the least positive integer which is a multiple of 31 and when divided by 15, 24 and 32 leaves the remainders 2, 11 and 19, respectively ?

(A) 2418
(B) 2387
(C) 2356
(D) 2325
(E) 2125


15 = 3 * 5
24 = 3 * 8
So, the options shouldn't be divisible by 3, 5 or 8
Eliminate (D) & (E) as they are divisible by 5.
Eliminate (A) as 2 + 4 + 1 + 8 = 15, which is divisible by 3
Eliminate (C) as last two digits(56) is divisible by 8
IMO, (B) - 2387
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Re: What is the least positive integer which is a multiple of 31 and when [#permalink] New post   05 Aug 2021, 11:57
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Since 15 - 2 = 13
24 - 11 = 13
32 - 19 = 13

The number would be in the form of LCM (15, 24, 32)*k - 13 = 480 * k - 13

The number is also a multiple of 31

=> k = 1 ; the number would be = 480 - 13 = 467 ........not divisible by 31
=> k = 2; the number would be = 480*2 - 13 = 947 .......not divisible by 31
=> k = 3; the number would be = 480*3 - 13 = 1427.......not divisible by 31
=> k = 4; the number would be = 480*4 - 13 = 1907.......not divisible by 31
=> k = 5; the number would be = 480*5 - 13 = 2387 ......Divisible by 31

So the required number is 2387

OA should be B
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What is the least positive integer which is a multiple of 31 and when [#permalink] New post   05 Aug 2021, 20:55
OA B
Lets the number we need to find is abcd
abcd: 15 left 2 remainder so d must be 2 or 7, only B match
so answer B
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What is the least positive integer which is a multiple of 31 and when [#permalink]
05 Aug 2021, 20:55
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