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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 21:44
To find: Remainder when integer X is divided by 40 i.e. X=40q+R, R=? Statement1: 3x+30 leaves a remainder 93 when divided by 120 i.e 3x+30=120q+93 =>3x=120q+63 => x=40q+21 therefore, remainder = 21 Sufficient to answer
Statement 2: 5x10 leaves a remainder 15 when divided by 20 i.e 5x10=20q+15 => 5x=20q+25 => x =4q+5 =>x=4(q+1)+1 (i.e remainder can't be greater than divisor) so possible x=1,5,9,13,................................,41,45,49,53............. for all above x values, remainders are different for each when divided by 40 i.e 1,5,9,13,...................,1,5,9,13,........ So, statement 2 is 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, 21:58
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, 22:43
(1) 3X + 30 leaves remainder 93 when divided by 120. First number that satisfies this is 93, 3x+30=93 => x=21. Next number would be 120+93=213; 213=3x+30=> x=61. possible values of x=21,61,101 so on. Each leave a remainder of 21 when divided by 40. Sufficient.(2) 5X  10 leaves remainder 15 when divided by 20. First number that satisfies this is 15, 5x10=15 => 5. Next number would be 15+20=35; 35=5x10=> x=9. x:5,9,13,17...... Rach when divided by 40 can leave different remainder. InsufficientAns. A
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Re: What is the remainder when X is divided by 40?
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17 Jul 2019, 23:07
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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18 Jul 2019, 00:12
(1) After all cancellations, it is given x= a*40+21, x =21, 61, 101, 141, 181,....... divide 40, some quotient and remainder 21, sufficient (2) After all cancellations, it is given x=b*4+5 x=5, 9, 13, 17, 21, 25............ divide by 40, remainder 5, 9, 17, 21, 25, etc , insufficient IMO A



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 00:12
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, 01:46
What is the remainder when x is divided by 40?
1) 3X + 30 leaves remainder 93 when divided by 120.
Let’s create the formula of this statement:
30x+30 = 120a + 93 30x = 120a + 63 x = 40a + 21
We can see that if 40a + 21 is divided by 40, then the remainder is 21. Therefore 1) is sufficient.
2) 5X  10 leaves remainder 15 when divided by 20.
Let’s create the formula of this statement:
5x – 10 = 20b + 15 5x = 20b +25 X = 4b + 5
We can see that if 4b + 5 is divided by 40, then the remainder is different depending on b. Therefore 2) is insufficient.
IMO A



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 02:27
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.
statement 1  3X+30 leaves remainder 93 when divided by 120 3X+3 can be written as 3(X+10)/120 = X+10/40 so this leaves remainder 93 So X/40 will leave remainder 93+10 = 103
Hence Statement one is sufficient
Statement 2 = 5X  10 leaves remainder 15 when divided by 20. 5X10 = 5(X2) 5(X2)/20 leaves remainder 15
Suppose X = 13 then if we multiply both denominator and numerator by 2 then 10(X2)/40 = 10*(132)/40 = 110/40 = 30 leaves remainder 30 Suppose X = 17 then if we multiply both denminator and numerator by 2 then 10(X2)/40 = 10(172)/40 = 10*15/40 = 150/40 leaves remainder 30.
Hence 5X10 leaves remainder 15 when divided by 20 , but it cannot be determined for sure what is the remainder when it X is divided by 40 Hence insufficient
Ther Answer is A



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 02:31
What is remainder when x/40? Formula for remainders is a/b=integer+r. We will apply this formula for both statements. 1. When 120 divides 3x+30, remainder is 93. Substitute number to formula above. (3x+30)/120=integer+93 3x+30=120*i+93 , we can multiply by 1/3 all sides to get easier numbers to calculate x=40*i+21, x/40=i+21, remainder is 21 A is good 2. When 20 divides 5x10, remainder is 15. Substitute number to formula (5x10)/20=integer+15 5x10=20*integer+15 , multiply by 1/5 x=4*integer+5 x/4=integer+5, different values possible. IMO A



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 02:31
(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, 03:15
What is the remainder when positive integer X is divided by 40?(1) 3X + 30 leaves remainder 93 when divided by 120.Let's imagine if we 3x+30 divide by 120 we have reminder of 83 are 21, 61, 101.... (arithmetic progression: add 40 to previous term) 21/40=21 is reminder, 61/40=21 is reminder and so on... Reminder is always equal to 21. Sufficient. (2) 5X  10 leaves remainder 15 when divided by 20.Let's imagine if we 5x10 divide by 20 we have reminder of 15 are 5, 9, 13... (arithmetic progression: add 4 to previous term) We've always got different reminders, so insufficient. A is the answer.
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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 03:35
(1) 3X + 30 leaves remainder 93 when divided by 120. (2) 5X  10 leaves remainder 15 when divided by 20. Statement1: (3x + 30  93)/120 is an integer Implies (x  21)/40 is an integer. Therefore reminder = 21. Sufficient. Statement2: (5x  10 15)/20 is an integer (5x25)/20 is an integer (x5)/4 is an integer Not sufficient since we cannot determine reminder when divided by 40. Option A.
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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 04:19
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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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 04:25
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: We have to find \(\frac{x}{40}\) = Q +\(\frac{R}{40}\)
From the first statement: \(\frac{(3x+30)}{120}\) = Q +\(\frac{93}{120}\)
\(\frac{x}{40}\) = Q +\(\frac{21}{40}\) Hence sufficient.
From Statement 2;
\(\frac{(5x10)}{20}\) = Q + \(\frac{15}{20}\)
\(\frac{x}{4}\) = Q +\(\frac{5}{4}\)
Hence insufficient. Therefore A IMO



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 04:48
Given : x=40a+r ..........................(1)
We need to find r.
(1) 3X + 30 leaves remainder 93 when divided by 120.
3x+30 = 120b+93 3(x+10) = 120b+93 x+10=40b+31 x=40b+21..........................(2)
If we compare equation (1) & (2) r=21 Sufficient.
(2) 5X  10 leaves remainder 15 when divided by 20.
5x10 = 20c+15 x2=4c+3 x=4c+5...................(3)
Equation (1) & (3) are not comparable. Insufficient.
So, Ans should be (A)



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What is the remainder when X is divided by 40?
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18 Jul 2019, 04:49
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.
Statement1:
3X+30=120*a+93 (a is quotient) 3X=120a+9330 3X=120a+63 3X/3=120a/3+63/3 X=40a+21 Well, if we divided X by 40, remainder will be 21. Sufficient
Statement2: 5X  10=20a+15 (a is quotient) 5X=20a+15+10 5X=20a+25 5X/5=20a/5+25/5 X=4a+5 Well, it depends on 'a' if we divide X by 40. if a≥8, the remainder will be 5. if a<8, the remainder will be different from 5. Insufficient
Answer choice is A.



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 06:57
What is the remainder when positive integer X is divided by 40?
X = 40*k + a a = ?
(1) 3X + 30 leaves remainder 93 when divided by 120. 3X + 30 = 120*k1 + 93 3X=120*k1+63 We know that X = 40*k + a 120 / 40 = 3, so 40 can be included in 120 3 times That's mean a = 23 SUFFICIENT (2) 5X  10 leaves remainder 15 when divided by 20. 5X  10=20*k2 + 15 5X = 20*(k2+1) + 5 As: X = 40*k + a 20 can be included in 40 2 times, so exists 2 possible remainders of a: a = 5 and a = 25 INSUFFICIENT
ANSWER A



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 07:23
Option A
(1) 3X + 30 leaves remainder 93 when divided by 120.
here 3x when divided by 120 will leave a remainder of 63 (ie 3 x 21).. In that case x when divided by 120 will leave a remainder of 21
(2) 5X  10 leaves remainder 15 when divided by 20. here 5x will leave a remainder of 5 when divided by 20... the are many possible values for such cases.. X can be 5, 9 etc... hence it is insufficient !!



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 07:27
Answer A Statement i= sufficient 3x+30=120k+93 x=40k+21 remainder 21 statement ii not sufficient 5x10=20I+15 x=4I+5, 5,13 are remaninders not sufficient



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Re: What is the remainder when X is divided by 40?
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18 Jul 2019, 07:52
X=40k+r where r is the remainder
Statement 1: 3X+30= 120k+3r+30 3r+30 = 93 3r=63 r=21 Sufficient.
Statement 2: 5X10=200k+5r10 Wen 5X10 is divided by 20, 200k is reduced to 10k. But we don't know about 5r10 If 5r10 <20, 5r10=15; r=5 If 5r10>20, lets say, 5r10 = 35, r=9 Not sufficient.
Hence, option (A).




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