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03 Dec 2018, 03:08
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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
A. 7
B. 30
C. 53
D. 76
E. 99
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
A. 7
B. 30
C. 53
D. 76
E. 99
Clearly option E..
99= 5*19+4 and 99=23*4+7
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
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
