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Sub 505 Level|   Remainders|      
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Bunuel
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x is a positive integer less than 100. When x is divided by 5, the rem 03 Dec 2018, 03:08
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E
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87% (01:44) correct 13% (02:17) wrong based on 215 sessions

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x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?


A. 7
B. 30
C. 53
D. 76
E. 99
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E
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x is a positive integer less than 100. When x is divided by 5, the rem 03 Dec 2018, 03:57
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Bunuel
x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?


A. 7
B. 30
C. 53
D. 76
E. 99

Clearly option E..
99= 5*19+4 and 99=23*4+7
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x is a positive integer less than 100. When x is divided by 5, the rem 03 Dec 2018, 15:47
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Bunuel
x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?


A. 7
B. 30
C. 53
D. 76
E. 99

x=5q+4
x=23p+7
→23p-5q=-3
if 5q has a 5 units digit,
then 23p must have a 2 units digit
try 4*23=92
92-5*19=-3 yes
p=4, q=19,
and n=99
E
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x is a positive integer less than 100. When x is divided by 5, the rem 11 Apr 2020, 00:35
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X=5a+4
X=23b+7

5a has to be divisible by 5 and total has to be less than 100, so a must have to be less than 20. Take a=19, that will give u value of X=99.
Now check second equation. Divide 99 by 23 and u will find a remainder of 7. As (23*4=92). So 99 works.

So ans is 99.
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x is a positive integer less than 100. When x is divided by 5, the rem 11 Apr 2020, 00:42
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Bunuel
x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?


A. 7
B. 30
C. 53
D. 76
E. 99

Take multiples of 23 & keep adding 7 to the number (<100). For every such number check if it's ending with 4 or 9.
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x is a positive integer less than 100. When x is divided by 5, the rem 11 Apr 2020, 05:58
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Only option when divided by 5 gives remainder 4 is 99, hence it is the answer choice

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x is a positive integer less than 100. When x is divided by 5, the rem 29 Apr 2020, 21:42
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Bunuel
x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?


A. 7
B. 30
C. 53
D. 76
E. 99

Use options.

Only option E, which is 99, gives us remainder 4 when divided by 5. NO need to check anything else.

Answer E
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x is a positive integer less than 100. When x is divided by 5, the rem 27 Dec 2024, 08:51
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When x is divided by 5, the remainder is 4

Dividend = Divisor * Quotient + Remainder

=> x = 5*k + 4 (where k is an integer)
=> x = 5k + 4

when x is divided by 23, the remainder is 7

=> x = 23t + 7 (where t is an integer)
=> x = 5k + 4 = 23t + 7
=> 5k = 23t + 3
=> k = \(\frac{23t + 3}{5}\)

Only those values of t which will give k also as an integer are the possible values
=> t = 4 and k = \(\frac{23*4 + 3}{5}\) = 19
=> n = 5k + 4 = 5*19 + 4 = 99

So, Answer will be E
Hope it helps!

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