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Does the integer k have at least three different positive

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Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 04:51
00:00

Question Stats:

75% (01:35) correct 25% (01:03) wrong based on 2 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

Diagnostic Test
Question: 42
Page: 26
Difficulty: 600


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Re: Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 04:51
SOLUTION

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Answer: C.
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Re: Does the integer k have at least three different positive [#permalink] New post 09 Jul 2012, 05:44
Bunuel wrote:
Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer.
(2) k/10 is an integer.

Hi,

For integer k to have atleast 3 different positive prime factors,
k = a.b.c, where a, b, c are prime numbers.

Using (1),
k/15 is an integer,
least value of k =15, which has two different prime factors 3 & 5. Insufficient.

Using (2),
k/10 is an integer,
least value of k =10 which has two different prime factors 2 & 5. Insufficient.

Using both,
least value of k =30 which has two different prime factors 2, 3 & 5. Sufficient.

Answer is (C)

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Re: Does the integer k have at least three different positive [#permalink] New post 13 Jul 2012, 03:53
SOLUTION

Does the integer k have at least three different positive prime factors?

(1) k/15 is an integer --> since k is divisible by 3*5=15, then it's divisible by 3 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(2) k/10 is an integer --> since k is divisible by 2*5=10, then it's divisible by 2 and 5, hence k has at least those two prime factors, though it might have more (consider k=30). Not sufficient.

(1)+(2) At least 3 primes are factors of k: 2, 3, and 5. Sufficient.

Answer: C.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: Does the integer k have at least three different positive [#permalink] New post 17 Jul 2012, 00:46
If a divides b, then all the primes in a along with their powers are in b
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Re: Does the integer k have at least three different positive   [#permalink] 17 Jul 2012, 00:46
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