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06 Jul 2023, 11:45
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C
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Difficulty:
45%
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Question Stats:
73% (02:35) correct
27%
(02:41)
wrong
based on 150
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How many positive two-digit integers have a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, and a remainder of 4 when divided by 5?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
06 Jul 2023, 12:08
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Answer should be C.
LCM of 2,3and5 is 30.
So we have three 2 digit numbers i.e 29,59 and 89 .
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LCM of 2,3and5 is 30.
So we have three 2 digit numbers i.e 29,59 and 89 .
Posted from my mobile device
06 Jul 2023, 18:01
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How many positive two-digit integers have a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, and a remainder of 4 when divided by 5?
The concept is very simple: If difference between divisor and remainder is constant, take LCM and subtract 1 from it.
eg,
Divisor - 2,3,5
Remainder - 1,2,4
2-1=3-2=5-4
In this case, LCM of 2,3,5 = 30
Common difference = 1
Total two digit numbers possible, 29, 59, 89
Option (C)
The concept is very simple: If difference between divisor and remainder is constant, take LCM and subtract 1 from it.
eg,
Divisor - 2,3,5
Remainder - 1,2,4
2-1=3-2=5-4
In this case, LCM of 2,3,5 = 30
Common difference = 1
Total two digit numbers possible, 29, 59, 89
Option (C)
