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the smallest integer k

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by sanju09 » Sat Sep 17, 2011 3:42 am
What is the smallest integer k such that k is a multiple of 2, (k + 1) is a multiple of 3; (k + 2) is a multiple of 5 and (k + 3) is a multiple of 7?
(A) 53
(B) 106
(C) 158
(D) 263
(E) 316


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by knight247 » Sat Sep 17, 2011 4:00 am
We can look at the answer choices straight away. K has to be a multiple of 2. That directly eliminates A and D

(B)k=106 so divisible by 2. k+1=107 not divisible by 3 so NO
(C)k=158 so divisible by 2. k+1=159 divisible by 3. k+2=160 divisible by 5. k+3=161 divisible by 7. YES
(E)k=316 so divisible by 2. k+1=317 not divisible by 3 so NO

Hence C
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