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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, 08:14
IMO A.
Statement 1: 3X + 30 leaves remainder 93 when divided by 120. The numbers in this form would be 93,213,333,453... X values for these would respectively would be  30,70,110,150... When these values are divided by 40, it always leaves a remainder as 30. Hence, this statement is sufficient.
Statement 2: 5X  10 leaves remainder 15 when divided by 20. The numbers in this form would be 15,35,55,75... X values for these would respectively would be  5,9,13,17... When these values are divided by 40, does not give a fixed value. Hence, this statement is not sufficient.



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:16
The question states that what is the remainder when X is divided by 40 Statement 1: 3X + 30 leaves remainder of 93 when divided by 120 Let X = 21, therefore, 3(21) + 30 = 93 Thus, 93/120 gives remainder of 93 therefore, 93/40 gives remainder of 13 Let X = 61, therefore, 3(61) + 30 = 213 thus, 213/120 gives remainder of 93 therefore, 213/40 gives remainder of 13 similarly, let X = 101, therefore, 3(101) + 30 = 333 thus, 333/120 gives remainder of 93 therefore, 333/40 gives remainder of 13 Therefore this statement is sufficient (AD) Statement 2: (5X  10)/20 gives remainder of 15 let X = 5, therefore (5x5  10)/20 = 15/20 gives remainder of 15 therefore, 5/40 gives remainder of 5 let X = 9, therefore (5x9  10)/20 = 35/20 gives remainder of 15 therefore, 9/40 gives remainder of 9 Not sufficient Hence answer choice A.
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 08:27
IMO A
Have to find: Remainder of \(X/40\)
Statement 1 > \(\frac{(3X + 30)}{120}\) gives a remainder of 93. Substitute for X based on this statement. For X = 21, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21. For X = 101, \(\frac{(3X + 30)}{120}\) gives the remainder of 93 and \(X/40\) gives a remainder of 21 again. > Sufficient
Statement 2 > \(\frac{(5X  10)}{20}\) gives a remainder of 15. Substitute for X based on this statement. For X = 5, \(\frac{(5X  10)}{20}\) gives the remainder 15 and \(X/40\) gives the remainder 5. For X = 9, \(\frac{(5X  10)}{20}\) gives the remainder 15, but \(X/40\) gives the remainder 9. > Insufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 09:44
To find,
Remainder of X when X is divided by 40.
We know,
Dividend = Divisor * Quotient + Remainder
Let us check the two options 
Option 1: 3X + 30 leaves remainder 93 when divided by 120.
=> 3*X + 30 = 120 * Quotient + 93 => X + 10 = 40 * Quotient + 31 => X = 40 * Quotient + 21
Hence, X whenever divided by 40 will give a remainder of 21.
Hence option 1 is sufficient.
Option 2: 5X  10 leaves remainder 15 when divided by 20.
=> 5*X  10 = 20 * Quotient + 15 => X  2 = 4 * Quotient + 3 => X = 4 * Quotient + 5 => X = 4 * Quotient + 4 + 1 => X = 4 * (Quotient + 1) + 1
Hence, X whenever divided by 4 will give a remainder of 1.
Now, if X is 5 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40. Now, if X is 9 (satisfying above condition in option 2) then it will give a remainder of 9 when divided by 40. Now, if X is 45 (satisfying above condition in option 2) then it will give a remainder of 5 when divided by 40. Now, if X is 53 (satisfying above condition in option 2) then it will give a remainder of 13 when divided by 40.
Hence, option 2 is 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, 10:02
IMOA
Remainder when positive integer X is divided by 40
(1) 3X + 30 leaves remainder 93 when divided by 120.
3X+30= 120K + 93 => X+10= 40K + 31 [K = integer] => X21 = 40K => X21= { 0, 40, 80, ........40K} => X= 21, 61, 81,....40K+21 Remainder (X/40)= 21
Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. =>.5X10=20K+15 => 5X= 20K+25 => X= 4K+5 => X= {5,9,13,17...........4K+5} Remainder (X/40)= {5,9,13,17.....}
Not Sufficient



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 11:19
What is the remainder when positive integer X is divided by 40?
40q+r = X ..... q is quotient and r is remainder. We have to find r.
(1) 3X + 30 leaves remainder 93 when divided by 120.
120q+93 = 3X + 30 120q+63 = 3X 40q+21 = X ... This is in the same form as 40q+r=X
Therefore r = 21
(1) IS SUFFICIENT
(2) 5X  10 leaves remainder 15 when divided by 20.
20q+15 = 5X10
20q + 25 = 5X
4q + 5 = X
It is not possible to represent X in the form of 40q+r....
X could be 9 with remainder 9, or x could be 45 with remainder 5.
(2) IS NOT SUFFICIENT
ANSWER: A  1 Alone is SUFFICIENT



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 12:30
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, 14:17
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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What is the remainder when X is divided by 40?
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17 Jul 2019, 18:07
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, 19:48
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, 20:58
Given, X is a positive integer. We need to find the remainder of X/40.
(1) 3X + 30 leaves remainder 93 when divided by 120. 3X + 30 = 120 * A + 93, where A is the quotient 3X = 120*A + 63 > (a)
Substituting values of A in (a): A = 1 3X = 120 + 63 => X = 61 Remainder of \(\frac{X}{40}\) = \(\frac{61}{40}\) = 21 > [1]
A = 2 3X = 240 + 63 => X = 101 Remainder of \(\frac{X}{40}\) = \(\frac{101}{40}\) = 21 > [2]
From [1] and [2] we find the pattern will keep continuing. Thus, the Remainder of \(\frac{X}{40}\)is 21.
Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. 5X – 10 = 20 * B + 15, where B is the quotient. 5X = 20*B + 25 > (b)
Substituting values of B in (b): B = 1 5X = 20 + 25 => X = 9 Remainder of \(\frac{X}{40}\) = \(\frac{9}{40}\) = 9 > [3]
B = 2 5X = 40+ 25 => X = 13 Remainder of \(\frac{X}{40}\) = \(\frac{13}{40}\) = 13 > [4]
From [3] and [4] we find that it does not give a unique solution.
Not Sufficient
Answer A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 22:07
What is the remainder when positive integer X is divided by 40?
(1) 3X + 30 leaves remainder 93 when divided by 120.
Assume 'a' is the quotient. We can write 3X+30 as:
3X + 30 = 120*a + 93
simplify this for X, 3X = 120*a + 63 X = 40*a + 21.....................when X is divided by 40, remainder will be "21"
First can answer the question.
(2) 5X  10 leaves remainder 15 when divided by 20.
Just like we did in first part, assume 'b' is the quotient.
5X10 = 20*b +15 5X = 20*b + 25 = 20*(b+1) + 5
X = 4*(b+1) + 1......................from this we can not answer the question.
So, second can not answer the question.
ANSWER : A



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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 23:12
What is the reminder of \(\frac{x}{40}\) ? ST1. \(3x + 30\) leaves remainder \(93\) when divided by \(120\). If \(3x + 30 = 120k + 93\) is simplified, we get \(x = 40k + 21\). Now the question is what is the reminder of \(\frac{(40k + 21)}{40}\) ? If simplified we get \(k + \frac{21}{40}\), thus regardless of \(k\) the reminder is \(21\). SufficientST2. \(5x  10\) leaves remainder \(15\) when divided by \(20\). If \(5x10=20p + 15\) is simplified, we get \(x=4p+5\). Now the question is what is the reminder of \(\frac{(4p + 5)}{40}\) ? If \(p=1\), then the remainder is \(9\). If \(p=2\), then the remainder is \(13\). Insufficient Hence A
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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 01:31
(1) 3X + 30 leaves remainder 93 when divided by 120. > 3X + 30 = 120M + 93, for any integer M > 3X = 120M + 63 > X = 40M + 21
So, Remainder = 21
Sufficient
(2) 5X  10 leaves remainder 15 when divided by 20. > 5X  10 = 20N + 15, for any integer N > 5X = 20N + 25 > X = 4N + 5 > Possible values of X = 5, 9, 13, 17, . . . . .
So, Possible Remainders = 5, 9, 13, 17 . . . . .
Insufficient
IMO Option A
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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 03:19
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. Solution : Question Stem analysis:We are required to find out remainder when 40 is divided by X, IMP property : Dividend = Quotient X divisor + Remainder. Statement one analysis:We can form the equation using the above stated property, 3X + 30 = 120Q + 93. 3X = 120Q + 63 X= 40Q + 21 If we divide 40Q + 21 by 40, we know that 40Q is divisible by 40, and 21 when divided by 40 leaves a remainder of 21. Hence statement one alone is sufficient. we can eliminate C & E. Statement two alone:We can form the equation using the above stated property, 5X 10 =20Q + 15, 5X= 20Q+ 25 X = 4Q + 5 In this, we don't know if 40Q is divisible by 40, for eg, if Q=10, then yes we have a remainder of 5, if Q= 1, then the remainder is different. Hence without knowing the value of Q, this statement is insufficient. Answer must be A
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