If x is an integer with n distinct prime factors, is n greater than or

Question

If x is an integer with n distinct prime factors, is n greater than or equal to 3?

(1) x is divisible by 6.
(2) x is divisible by 10.

AdlaT · Answer

Solution: statement 1) x is divisible by 6. x=6--> prime factors 2 and 3. n=2<3. NO x=30-->prime factors 2,3 and 5. n=3=3.YES x=210-->prime factors 2,3,5 and 7. n=4>3 YES. Hence Not sufficient. statement 2) x is divisible by 10. x=10-->prime factors 2 and 5. n=2<3. NO x=30-->prime factors 2,3 and 5. n=3=3 YES x=210-->prime factors 2,3,5 and 7. n=4>3 YES Hence Insufficient. statement 1) and statement 2) together. LCM of 10 and 6 is 30. x=30--> prime factors are 2,3 and 5. n=3=3 YES. x=210-->prime factors are 2,3,5,and 7. n=4>3 YES. Always , n>=3 Hence together Sufficient. ANS C.

gmat201567 · Answer

Given, x is an integer and x has distinct prime factors.
so x = p1^a * p2^b * pn^z
Q is n>=3

(i)x is div by 6
6 = 2*3; x=2^a * 3^b * ..pn^z
X can have 2 or more than 2 prime factors.
Not sufficient

(ii)x is div. by 10
10 = 2*5; x=2^a * 5^b * ..pn^z
X can have 2 or more than 2 prime factors.
Not sufficient

(i)+(ii)
x = 2^a * 3^b * 5^c * ..pn^z
X definitely has 3 or more than 3 different prime factors.

If x is an integer with n distinct prime factors, is n greater than or

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia