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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:34
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What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. (2) 5X - 10 leaves remainder 15 when divided by 20.
(1) 3X + 30 leaves remainder 93 when divided by 120. 3X+30 = 120k+93 3X = 120k +63 X=40k+21 21 is the remainder when positive integer x is divided by 40 SUFFICIENT
(2) 5X - 10 leaves remainder 15 when divided by 20. 5X-10 = 20k + 15 5X = 20K + 25 = 20Y+5 X = 4Y+1 NOT SUFFICIENT
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17 Jul 2019, 08:31
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What is the remainder when positive integer X is divided by 40?
This is an easy question. Nothing to analyze in the stem lets move to the statements.
(1) 3X + 30 leaves remainder 93 when divided by 120. This choice is correct, cause X will take values like 39, 79, etc, which will always have remainder as 39. Hence this is sufficient.
(2) 5X - 10 leaves remainder 15 when divided by 20. This statement is insufficient. Cause X will have multiple values like 5, 9, etc and hence the remainder will also be different.
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17 Jul 2019, 08:35
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IMO answer is A:
we know from statement 1: 3x+30 = 93, x= 21, similarly 3x+3 = 213, x = 61. so x can be 21, 61,101,.... In all these cases, we get a reminder of 21 when x is divided by 40. so suff
from statement 2: in similar lines, x can be 5,9,13,17,21,25... as multiple values, multiple reminders, not suff
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17 Jul 2019, 08:37
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(1) 3X + 30 leaves remainder 93 when divided by 120. Sufficient. 3x+30=120k+93 3x=120k+63 x=40k+21 Thus remainder will be 21 (2) 5X - 10 leaves remainder 15 when divided by 20. Not sufficient. 5x-10=20m+15 5x=20m+25 x=4m+5 Thus we have plenty of possible remainders: 5, 9, 13...
Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:53
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A.
From st 1, mathematically it can be written as, 3x+30 = 120n1+93 => x = 40n1 + 21, clearly remainder is 21 when x is divided by 40 - Sufficient
From st 2, mathematically it can be written as, 5x-10 = 20n2+15 => x = 4n2 + 5, so can have values such as 9, 13,17 .. which are all remainders when x is divided by 40 - Not Sufficient
Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:04
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What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. - Sufficient, Min X Number that satisfies the requirement is (93-30)/3=21 which leaves a remainder of 21 when divided by 40. When X=181 (21+40*4) the above becomes (543+30)/120 still gives a remainder of 93 when divided by 120 and 21 when divided by 40. Remainder will always be 21
(2) 5X - 10 leaves remainder 15 when divided by 20. Insufficient; When Min X Number that satisfies the requirement is (25-10)/3=5 which leaves a remainder of 5 when divided by 40; When X=9 also satisfies the requirement but gives a remainder of 9 when divided by 40. Two values for X have 2 different remainders
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17 Jul 2019, 09:05
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3x+30 when divided by 120 leaves a remainder 93 i.e 3x+30+27 (120-93=27) is divisible by 120 3x+57 is divisible by 120 3(x+19)is divisible by 120 x+19 is divisible 40 i.e 21 is the remainder hence A is sufficient
5x-10 leaves remainder 15 when divided by 20 ie 5x-5 is divisible by 20 5(x-1) is divisible by 20 x-1 is divisible by 4 but we calculate the remainder when x is divided by 40 Hence insufficient
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17 Jul 2019, 09:09
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Answer is A
Question is asking what is the remainder when positive integer X is divided by 40?
St.1 - 3X + 30 leaves remainder 93 when divided by 120. If the number is 93 then X=21, then X/40 remainder is 21. Lets try with another number that satisfies the condition, X=61, then 61*3+30=213/120 Remainder is 93, then X/40 Remainder is 21. In both the cases X/40 remainder is 21. Sufficient.
St.2 - 5X - 10 leaves remainder 15 when divided by 20. If the number is 15 then X=5, then X/40 remainder is 5, but if the number is 35 then X=9, then X/40 remainder is 9. Two different answers therefore the statement is Insufficient.
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