What is the least number when divided by 8, 12, 20 and 30 leaves a remainder 4 and when divided by 21 leaves a remainder 7 ?
A. 124
B. 360
C. 364
D. Cannot be determined
Answer: Option C
Solution(By Examveda Team)
Lcm of 8, 12,20,30 is 120. As they leave a remainder 4 So it should be 120 + 4. But when being divided by 21, remainder is 7 So the number will be exactly divisible by (21 + 7) = 28. The number will be in the form of (120k + 4) which is divisible by 28 Where k is any positive integer. Now, if we divide 120 by 28, the remainder is 8 We need a remainder of 24, because (24 + 4) = 28 Now (8 × 3) = 24 Thus, k = 3 Hence, the number would be (120 × 3) + 4 = 364Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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