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What is the remainder when X is divided by 40?
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17 Jul 2019, 07:00
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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.
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:34
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. 5X10 = 20k + 15 5X = 20K + 25 = 20Y+5 X = 4Y+1 NOT SUFFICIENT
IMO A




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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:08
Case A 3x + 30 = 120y + 93 x + 10 = 40y + 31 So, x = 40y + 21 Sufficient
Case B 5x  10 = 20y + 15 x2 = 4y + 3 x=4y+5, Insufficient A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:26
Quote: 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.
Option D



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:27
both together are sufficient. C is the right answer IMO
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:31
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.
Hence the answer choice A is correct.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:33
Statement 1
3x+30=120m+93
X= 40k+ 21, thus when divided by 40, will leave 21
Statement 2 5x10 = 20k + 15
X= 4k + 5
Not sufficient
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:35
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
so A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:37
(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. 5x10=20m+15 5x=20m+25 x=4m+5 Thus we have plenty of possible remainders: 5, 9, 13...
IMO A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:38
Answer is: D. both statements are sufficient.
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120. X must be odd. (2) 5X  10 leaves remainder 15 when divided by 20.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:44
From A 3x + 30 = 120A +93 (where A is an positive integer) 3x = 120A +63 x = 40A +21
Divide (40A +21)/40 Remainder = 21
A is sufficient.
From B
5x 10 = 20B +15 (Where B is positive integer) 5x = 20B +25 X = 4B +5
divide (4B +5)/40 Take B=40 Then Remainder = 5 Take B as 1 then Remainder = 9
No single answer B is insufficient
Only A can sufficiently gives the answer.
Hence A is the answer.



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What is the remainder when X is divided by 40?
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Updated on: 17 Jul 2019, 18:57
What is the remainder when positive integer X is divided by 40?
From (1) 3X + 30 leaves remainder 93 when divided by 120:
3X +30 = 120K+93
X+ 10 = 40K+ 31
X = 40K + 21, so remainder will be always 21
So,sufficient
From (2) 5X  10 leaves remainder 15 when divided by 20:
5X 10 = 20K+15
5X = 20K + 25
x = 4K + 5
So reminder will vary based on value ok K, so not sufficient.
(A) is the answer.
Originally posted by Mizar18 on 17 Jul 2019, 07:44.
Last edited by Mizar18 on 17 Jul 2019, 18:57, edited 1 time in total.



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What is the remainder when X is divided by 40?
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Updated on: 17 Jul 2019, 09:18
For 1: \(\frac{3X+3093}{120}\) =y X+1031=40y X21=40y
So, remainder is 21 Sufficient
For 2: \(\frac{5X1015}{20}\) =y X23=4y X5=4y Insufficient
Hence A
Originally posted by kitipriyanka on 17 Jul 2019, 07:48.
Last edited by kitipriyanka on 17 Jul 2019, 09:18, edited 1 time in total.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 07:53
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, 5x10 = 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



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:03
X = 40k + N, we are asked to find the remainder:
1. 3X + 30 leaves remainder 93 when divided by 120. 3X + 30 = 120k +93 3X = 120k + 63 If K = 1 , 3X = 183 => X = 61 If K = 2, 3X = 303 => X = 101 Not Sufficient.
2. 5X  10 leaves remainder 15 when divided by 20. 5X  10 = 20k + 15 5X = 20k + 25 If K =1, 5X = 45 => X = 9 If K = 2, 5X = 65 = > X = 13
Not sufficient.
Thus we can't find a unique number which will give us a unique remainder.
IMO the answer is E.
Please hit kudos if you like the solution.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:04
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 (9330)/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 (2510)/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
IMO A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:05
3x+30 when divided by 120 leaves a remainder 93 i.e 3x+30+27 (12093=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
5x10 leaves remainder 15 when divided by 20 ie 5x5 is divisible by 20 5(x1) is divisible by 20 x1 is divisible by 4 but we calculate the remainder when x is divided by 40 Hence insufficient
IMO A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:09
Answer is AQuestion 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. Answer is A
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:10
Correct answer is A; explanation is given in the attachment
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:11
Quote: 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. GIVEN: rof x/40? (1) 3X + 30 leaves remainder 93 when divided by 120: 3x+30/120 rof 93… 3x+30={93,213,333,453,…} x={21,(fraction),101,141…}; rof x/40={21,21,21…} sufficient. (2) 5X  10 leaves remainder 15 when divided by 20: 5x10/20 rof 15… 5x10={15,35,55,75,…} x={5,9,13…}; insufficient. Answer (A).




Re: What is the remainder when X is divided by 40?
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