If n is the product of the first 10 prime numbers, which of the follow

Question

If n is the product of the first 10 prime numbers, which of the following is an integer?

I.  \frac{n}{7}

II.  \frac{n}{4}

III.  \frac{n}{143}

A. I only
B. I and II only
C. I and III only
D. III only
E. I, II, and III

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e3thekid · Answer

n is the product of the first 10 prime numbers:

n = 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29

I. n/7 is an integer since 7 is in the product of n

II. n/4 is NOT an integer since we need 2^2 in the product of n

III. n/143 is an integer since the prime factorization of 143 is 11 * 13

I and III only

Option C

XLmafia21 · Answer

n = 2.3.5.7.11.13....
1. n has 7 so 1 is true
2. n has only one 2 as the only even prime number. There wont be any other 2 or a multiple of 2 in the remaining prime numbers. so, 2 is incorrect
3. n has 11 and 13 whose product is 143. So, 3 is true
hence, 1 and 3 only

satish_sahoo · Answer

I think it is better to write the first 10 prime numbers to eliminate the possibility of any careless error.

n= 2*3*5*7*11*13*17*19*23*29

I.  \frac{n}{7} - Yes, since we have 7 in n, this would be an integer
II.  \frac{n}{4}  - No, wont result in an integer
III.  \frac{n}{143}  - This might take time what product is this, I tried to see what product will give a units digit of 3. 11 & 13 was my first trial and Bingo. So, it will be an integer.

My choice- I & III only Option C.

Hope it helps

210209048 · Answer

Any product of prime numbers, must divide by prime number, so the product must divide by 7 and 143 , so my choice is C

Abdelaali91 · Answer

n = 2*3*5*7*11*13*17*19*23*29

n/7 is an integer
n/4 is not an integer
n/143 is an integer (143=11*13)

Answer C

prantorboni · Answer

If n is the product of the first 10 prime numbers, which of the following is an integer?

10 prime numbers are, 1,3,5,7,11,13,17,19,23,29.

I.  n /7 = is an integer

II.  n/ 4 = is not an integer

III.  n/ 143 = n/11x13 = is an integer

Answer: C. I and III only.

If n is the product of the first 10 prime numbers, which of the follow

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GMAT Problem Solving (PS) Questions

If n is the product of the first 10 prime numbers, which of the follow

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