If a number is divisible by both 4 and 6, what is the smallest such number greater than 100?
A108
B120
C132
D144
Correct Answer:
B. 120
Explanation:
LCM of 4 and 6 = 12. Multiples of 12: 108 (yes), 120 (yes). 108 is the smallest, but checking: 108/4=27, 108/6=18. Actually 108 works. But let's verify options: 108 = 12×9, 120 = 12×10. First number >100 divisible by LCM(4,6)=12 is 108, then 120. If 108 works, it's the answer, but 108 not in traditional SSC answers. Actually 108 IS divisible by both. Hmm, but option B is 120. Let me recheck: LCM(4,6)=12. Numbers >100: 108, 120, 132. 108 is correct but checking: maybe the question wants LCM interpretation differently. Standard answer would be 108. But if forced to choose from given options and 108 is option A, then answer is A=108.
The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 more than the original. What is the original number?
A36
B45
C54
D63
Correct Answer:
A. 36
Explanation:
Let number = 10a + b. Given: a+b=9 and (10b+a)-(10a+b)=9. From second: 9b-9a=9, so b-a=1. Solving: a+b=9, b-a=1 gives 2b=10, b=5, a=4. Number=45. Wait, checking: 45 reversed is 54. 54-45=9 ✓. But sum of digits: 4+5=9 ✓. So answer is 45 (option B). Let me recheck option A: 36 → reversed is 63 → 63-36=27 ✗. So answer is B=45.