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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 13:14
What is the remainder when positive integer X is divided by 40? (1) 3X + 30 leaves remainder 93 when divided by 120. 3x + 30 = 3(x + 10) / 120  remainder 93 = x + 10 / 40  remainder 13 = x / 40 remainder 3 Sufficient.
(2) 5X  10 leaves remainder 15 when divided by 20. If divided by 20 we get remainder 15 but we do not know the number. the number can be 15 or 35 if divided by 40 to the above numbers we get different remainders but if divided by 20 we get the same remainder. Insufficient.
Answer: A
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 13:27
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120 3x +30=120q + 93 3x 63 =120q —> (3x 63)/120=q Quotient =Integer ,Only when x= 21 , (3(21)63)/120=Integer So 21/40 have a remainder of 21 (Sufficient)
(2) 5X  10 leaves remainder 15 when divided by 20 5x10 =20q —> (5x10)/20= q (5(2)10)/20=Integer (5(6)10)/20=Integer .: x=2,6... (Not sufficient) as 2/40 and 6/40 gives different remainders
Answer A
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 13:30
Statement 1 3x+30= 120k+93, where k is nonegative integer. x+10=40k+31 x= 40k+21
We will always get 21 as a remainder, when x is divided by 40. Sufficient
Statement 2 5x10=20a+15, where a is nonnegative integer x2=4a+3 x=4a+5
Hence, x can be 5, 9, 13, 17...and so on If x=5, we will get 5 as a remainder, when x is divided by 40. If x=9, we will get 9 as a remainder, when x is divided by 40.
Insufficient.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 14:57
Answer D: both are sufficient solving first and 2nd equation we derive a equation which is enough to tell the solution that both are sufficient to tell remainder



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 15:06
What is the remainder when positive integer X is divided by 40?
Remainder of X/40 = ?
(1) 3X + 30 leaves remainder 93 when divided by 120.
Using remainder theorem, 3X + 30 = Q120 + 93, > 3X = Q120 + 63 or X = 40Q + 21, X = 61, 101, 141, etc for Q = 1, 2, 3, etc. In each of these cases, Remainder of X/40 will be equal to 21. Hence, sufficient.
(2) 5X  10 leaves remainder 15 when divided by 20.
5X  10 = Q20 + 15, > 5X = Q20 + 25 or X = (Q20 + 25)/5
X = 9, 13, 17, 21, etc...for Q = 1,2,3,4, etc, > Different remainder values possible for X/40. Hence not sufficient.
Correct answer A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 15:17
We are to find the remainder when a positive integer x is divided by 40.
1. 3x +30 leaves a remainder of 93 when divided by 120. (3x+30)/120 = 120m + 93 (X+10)/40=40m+31 If m=0 x+10=31 hence x=21 21/40 leaves R=21 If m=1, x+10=71 hence x=61 61/40 leaves R=21 If m=10, x+10=431 hence x=421. 421/40 leaves R=21. Therefore statement 1 on it’s own is sufficient.
2: 5x10 leaves Remainder of 15 when divided by 20. (5x10)/20= 20m+15 (x2)/4 = 4m + 3 When m=0 x2=3 hence x=5 5/40 leaves R=5 When m=1, x2=7 hence x=9 9/40 leaves a remainder of 9. Hence not sufficient.
The answer is therefore A.
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 15:17
We are to find the remainder when a positive integer x is divided by 40.
1. 3x +30 leaves a remainder of 93 when divided by 120. (3x+30)/120 = 120m + 93 (X+10)/40=40m+31 If m=0 x+10=31 hence x=21 21/40 leaves R=21 If m=1, x+10=71 hence x=61 61/40 leaves R=21 If m=10, x+10=431 hence x=421. 421/40 leaves R=21. Therefore statement 1 on it’s own is sufficient.
2: 5x10 leaves Remainder of 15 when divided by 20. (5x10)/20= 20m+15 (x2)/4 = 4m + 3 When m=0 x2=3 hence x=5 5/40 leaves R=5 When m=1, x2=7 hence x=9 9/40 leaves a remainder of 9. Hence not sufficient.
The answer is therefore A.
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 15:23
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.
x=40y+Z we need to find Z
From the first statement we have: 3X+30 = 120K+93 X+10=40K+31 X= 40K+21
So the remainder will be 21. Sufficient
From the second statement we have: 5X10 = 20F+15 X2=4F+3 X=4F+5
We can't define the reminder of X when divided by 40. Insufficient
The answer is A



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What is the remainder when X is divided by 40?
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Updated on: 18 Jul 2019, 15:53
1) 3*x+30 = 120*q + 93. Rearranging for x: x + 10 = 40*q + 31, x = 40*q + 21. Therefore, the remainder when x/40 = (40*q+21)/40 is always 21.
2) 5*x  10 = 20*q + 15. Rearranging for x: x  2 = 4*q + 3, x = 4*q + 5 Therefore, the remainder when x/40 = (4*q + 5)/40 is could be 5, 9, etc..
Answer is A.
Originally posted by leemoon on 17 Jul 2019, 18:25.
Last edited by leemoon on 18 Jul 2019, 15:53, 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, 18:31
#1 3X + 30 leaves remainder 93 when divided by 120. x=21,61 remainder would be when divided by 40 ; 19,21 insufficient #2 5X  10 leaves remainder 15 when divided by 20. X=5,13 remainder when divided by 40 ; 5,13 insufficient from 1&2 we dont have anything in common IMO E 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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What is the remainder when X is divided by 40?
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17 Jul 2019, 19:07
Question: What is the remainder when positive integer X is divided by 40?
(1) (3X + 30) leaves remainder 93 when divided by 120. \((3X + 30) = 120Q + 93\), where \(93\) is the remainder and positive integer quotient \(Q \geq{0}\) <=> \(X = 40Q + 21\) Therefore, when positive integer X is divided by \(40\), the remainder is \(21\) SUFFICIENT
(2) (5X  10) leaves remainder 15 when divided by 20. \((5X  10) = 20Q + 15\), where \(15\) is the remainder and positive integer quotient \(Q \geq{0}\) <=> \(X = 4Q + 5\) We only know that when positive integer X is divided by \(4\), the remainder is \(5\) . Unfortunately, we have no sufficient information on what the remainder is when positive integer X is divided by \(40\). NOT SUFFICIENT
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, 19:37
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120.Sufficient
3X+30 /120 with remainder 93 , 3X+30 = 120A+93
Case 1: A =0 for remainder to be 93 minimum 3X+30 = 93 => 3X = 63 => X = 21 Remainder of X /40 = 21
Case 2: A=1 3x+30 = 21x ==> X = 61 Remainder of X/40 = 21 So remainder of X /40 = 21 > Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. 5X10 = 20B+15 Case 1: B = 0 5X10 = 15 ===> X =25/5 = 5
Remainder for X /40 =5
Case 2 :B =1 5X10 = 20+15 => X =35/5 =7
Remainder for X/40 = 7
Case 3: B=2 5X10 =20*2+15 => X =55/5 = 11
Remainder for X/40 =11 So here remainder keeps changing So not Sufficient
Option A is the Correct Answer



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 19:48
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 divided by 120 remainder of 30 is 30 when divided by 120. remainder of 3x is 63 when divided by 120. remainder of x/40 =21 sufficient
2)remainder of 10/20 is 10 remainder of 5x is 5 when divided by 20 remainder of x/4 is 5 remainder of x/40 is 50 sufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 20:01
The answer is A St:13X+30=120k+93 3X=120k+63 X=40k+21 Therefore when divided by 40 remainder will be 21. St:2 5X10=20K+15 5X=20K+25 X=4K+5 Now when divided by 40 the remainder can be as follows : When K=1 ,X=9 and remainder =9 When K=10,X=45 and remainder=5 Therefore not sufficient
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 20:48
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.
We need to find remainder when \(\frac{x}{40}.\)
St 1) \(\frac{3x+30}{120}\)= q+93 (get rid of 120) 3x+30=120q+93 3x=120q+63 (divide by 3) x=40q+21 Now let's plug in some number for q. If q=0, x is 21 (remainder when \(\frac{x}{40}\)) If q=1, x is 61 (\(\frac{61}{40}\) remainder is 21) If q=2, x is 101 (\(\frac{101}{40}\) remainder is again 21) For any number substituted for q, we will always get remainder of 21 because q is multiple of 40 and thus will divide 40 evenly leaving remainder of 21 always. Thus, st 1 is sufficient
St 2) \(\frac{5x10}{20}\)=q+15 (get rid of 20) 5x10=20q+15 5x=20q+25 (divide by 5) x=4q+5 If q=0, x is 5 (\(\frac{5}{40}\) remainder is 5) If q=1, x is 9 (\(\frac{9}{40}\) remainder is 9) We already have two different values, thus st 2 is NOT sufficient 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, 20:53
X = 40k + r What is r?
1) 3X+30 = 120a +63
3X = 120a + 63 X=40a+21 . So remainder is 21, sufficient
2) 5X  10 = 20b + 15 X = 4b+5 X can be 5,9,13,17 or 45 etc. Remainder of each of these numbers when divided by 40 is different. Insufficient.
So, A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 20:55
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.
to find X = 40 K +R where R is the remainder
now using first given 3X + 30 = 120K+93 or 3X = 120K+63 or X = (120k + 63)/ 3 now we need remainder when divided by 40 thus X/40 = (120k + 63)/ 3*40
this will 120k will be completely divided by 120 and 6 will be the remainder when divided by 120 thus A is suffiencient
for given eq 5X  10 = 20K +15 or 5X = 20K+25 or X = (20K+25)/5 divided each side by 40 x/40 = (20K + 25)/5*50 now 20 is not completely divisible by (250) hence we cant determine the exact remainder without knowing K Thus B is not sufficient
Hence answer is A



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What is the remainder when X is divided by 40?
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Updated on: 17 Jul 2019, 20:59
We are asked to find the remainder when positive number X is divided by 40
St 1: \(\frac{3X + 30}{120}\)= Q + \(\frac{93}{120}\) (where Q is the quoitent) ==> X = 40Q + 21 ==> \(\frac{X}{40}\) = \(\frac{40Q}{40}\) + \(\frac{21}{40}\) ==> sufficient since our remainder will always be 21 no matter the value of Q
St 2: \(\frac{5X  10}{20}\) = Q + \(\frac{15}{40}\) ==> X = 4Q + 5 ==> \(\frac{X}{40}\) = \(\frac{4Q}{40}\) + \(\frac{5}{40}\)==> insufficient since we will getdifferent numbers for the remainder depending on the value of Q
The answer is A
Alternate solution
St 1: since our remainder is 93, it means that 3X + 30 could equal 93, 213, 333, etc ==> solve for X to find that X could be 21, 61, 101, etc, which all give a remainder of 21 when divided by 40 ==> sufficient
St 2: since our remainder is 15, it means that 5X  10 could equal 15, 35, 55, 75, etc ===> solve for X to find that X could be 5, 9, 13, 17, etc, which all give different remainders when divided by 40 ==> insufficient
Originally posted by bebs on 17 Jul 2019, 20:55.
Last edited by bebs on 17 Jul 2019, 20:59, 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, 20:57
Remainder when \(\frac{X}{40}\) ?
(1) 3X + 30 leaves remainder 93 when divided by 120. 3X+30 = 120 *Q +93 3X = 120 *Q +63 X = 40*Q + 21 This is exactly what is asked. when divided by 40 , remainder is 21 . so, sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. 5X10 = 15Q + 20 5X = 15Q + 30 X = 3Q + 15 X = 15, 18, 21, 24, ... If these are divided by 40 , then remainder could be 15, 18, 21, 24... hence, not sufficient
A is the answer !



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 21:06
Statement 1 is sufficient and statement 2 is not. 3X+30=120y+93 which gives X=40Y+21 so 21 would be remainder.
by solving statement 2, we get X=4Z+7. So, we are not sure about the remainder here.
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