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SAT Question of the Day July 30th 2013

### All numbers divisible by both and are also divisible by which of the following?

### A.

### B.

### C.

### D.

### E.

### This is a number set property question asking us about the divisibility of a set of numbers that are divisible by both 4 and 15.

### If a number is divisible by 4 it is also divisible by 2 (1, 2, 4, and the number itself). If this number is also divisible by 15 it is divisible by 3 and 5 (1, 3, 5, 15, and the number itself).

### If it is divisible by both it is divisible by any combination of 4 and 15 prime divisors (1, 2, 2, 3, and 5).

### The only number that does NOT have any additional prime divisors is 6. 8 (1, 2, 2, 2) has another 2 as its prime divisors. 18 has an additional 3 (1, 2, 3, 3). 24 has an additional 2 (1, 2, 2, 2, 3) and 45 has an additional 3 (1, 3, 3, 5).

### 56% of 192,000 got it right.

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