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25 Nov 2021, 09:45
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A
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Difficulty:
45%
(medium)
Question Stats:
73% (01:58) correct
27%
(02:17)
wrong
based on 199
sessions
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What least number must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 in each case is 7 ?
(A) 39
(B) 44
(C) 51
(D) 129
(E) 141
(A) 39
(B) 44
(C) 51
(D) 129
(E) 141
25 Nov 2021, 11:02
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There are other ways to do these kinds of problems when the answer choices aren't so convenient, but here we know, after subtracting, that our remainder must be 7 when we divide by 10, so the units digit will need to become 7, and we must be subtracting something ending in '9'. That means either 39 or 129 is correct, but those two numbers differ by 90, a multiple of 9 and of 15, so we'll get the same remainders by 9 and by 15 when we subtract either of them from 1936, and since we want to subtract the smallest possible number, 39 must be the answer.
27 Mar 2024, 04:47
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
What least number must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 in each case is 7 ?
1936 - a number should give us 7 as remainder when divided by 10
Concept: Remainder by 10 of any number = units' digit of that number
=> Units' digit of 1936 - a number = 7 => we are looking for a unit's digit of 9 in the option choices
=> We can eliminate B, C, E
Let's take 39 as we are trying to find the least number
1936 - 39 = 1987
Division by 9: Remainder of a number when divided by 9 = Remainder of sum of the digits by 9
=> Remainder of 1 + 9 + 8 + 7 = Remaidner of 25 by 9 = 7 => TRUE
Division by 10: Unit's digit = 7 => Remainder of 1987 by 10 = 7 => TRUE
Division by 15: Let's divided directly by 15, we will find that 1890 is dividible by 15
=> Remainder of 1987 by 15 = 7 => TRUE
So, Answer will be A
Hope it helps!
Watch the following video to MASTER Remainders
What least number must be subtracted from 1936 so that the remainder when divided by 9, 10, 15 in each case is 7 ?
1936 - a number should give us 7 as remainder when divided by 10
Concept: Remainder by 10 of any number = units' digit of that number
=> Units' digit of 1936 - a number = 7 => we are looking for a unit's digit of 9 in the option choices
=> We can eliminate B, C, E
Let's take 39 as we are trying to find the least number
1936 - 39 = 1987
Division by 9: Remainder of a number when divided by 9 = Remainder of sum of the digits by 9
=> Remainder of 1 + 9 + 8 + 7 = Remaidner of 25 by 9 = 7 => TRUE
Division by 10: Unit's digit = 7 => Remainder of 1987 by 10 = 7 => TRUE
Division by 15: Let's divided directly by 15, we will find that 1890 is dividible by 15
=> Remainder of 1987 by 15 = 7 => TRUE
So, Answer will be A
Hope it helps!
Watch the following video to MASTER Remainders
