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Question

Let E=[13+150]+[13+250]+...+ up to 50 terms, then which of the following is true?
Here [] denotes the greatest integer function.

A
E is divisible by exactly 2 primes
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B
E is prime
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C
E30
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D
E35
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Solution

The correct options are
A E is prime
C E30
For 1x33,13<13+x50<1
Since, 13+150=0.3333..+0.02=0.35333.. and 0.3333<0.3533<1
Also, 13+3350=0.3333..+0.6666=0.99999.. and 0.3333<0.9999<1
Therefore, 13+x50=0 for 1x33
For 34x50, 1<13+x50<43
Therefore, 13+x50=1 for 34x50
Thus E=0+0+......+0+1+1+...1=17
Hence, E30 and E is prime.

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