If x is an integer divisible by 15 but not divisible by 20, then x

Question

If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following?

A. 6 
B. 10 
C. 12 
D. 30 
E. 150

BrentGMATPrepNow · Accepted Answer

There are at least two different ways to solve this question: 
1) Determine what properties of x are required so that x is divisible by 15 but not divisible by 20, and then use those results to identify the correct answer 
2) Test values

When it comes to solving Integer Properties questions,  testing values  is often a very fast and effective approach. So let's do that.

Important: The question asks "x CANNOT be divisible by which of the following?"
So if we can show that x CAN be divisible by a certain value, we can ELIMINATE that answer choice.

If x is divisible by 15 but not divisible by 20, then x COULD be  30 
Check the answer choices....
Since  30  IS divisible by 6, 10 and 30, we can ELIMINATE answer choices A, B and D

Now let's test another possible value of x

If x is divisible by 15 but not divisible by 20, then x COULD be  150 
Since  150  IS divisible by 150, we can ELIMINATE answer choice E.

By the process of elimination, the correct answer is C

Cheers, 
Brent

Nikkb · Answer

as per my understanding
x is divisible by 15 => so x has a 3 and 5 in it ( as 15 =3*5)
but x is not divisible by 20 => as 20 = 2*2*5.. and x already has a 5 in it by above statement than:
either x does not have a 2 in it making x divisible by 2*5=10 but not by 20
or x does not have a 4 in it making x divisible by 5 but not by 20

Find x cannot be divisible by which number ?
Now we have to find a Must be condition , so it need to be true always.

Going by options:
A) 6 => 2*3 => x already have a 3, it can or cannot have a 2
B)10 => 2* 5 => x already have a 5, it can or cannot have a 2
C) 12 => 3*4 => x already have a 3, it cannot have a 4 in it. As if x have a 4 in it x will become divisible by 20.  Answer 
D) 30 => 3*2*5 => x already have a 3 and 5, it can or cannot have a 2
E) 150 => 15*2*3 => x already have a 15, it can or cannot have additional 2 and 3 in it.

So Answer: C

JeffTargetTestPrep · Answer

Since x is divisible by 15 and not 20, and 15 = 5 x 3 and 20 = 2^2 x 5, we see that x will never be divisible by a number with two 2s in its prime factorization. Thus, x will not be divisible by 12, because 12 = 2^2 x 3^1.

Answer: C

CrackverbalGMAT · Answer

If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following?

X is divisible by 15 => X is divisible by 3 and 5
X is not divisible by 20 , where 20 =5 * 4

Since we already know that X is divisible by 5, we can now conclude that X is not divisible by 4 . Otherwise X would have been divisible by 20.

Then x CANNOT be divisible by which of the following 
A. 6
B. 10
C. 12
D. 30
E. 150

If you analyze the options, we can say that X will not be divisible by 12 as 12 = 3*4
If X is divisible by 12, that means X should be divisible by 4 ,but it's is not.

Another approach would be assume a value for X and eliminate the options accordingly.
Assume X = 150 which is divisible by 15 but not by 20
150 is divisible by 6,10,30,150 but not by 12.

So option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

napolean92728 · Answer

Given Conditions
 
 x is an integer 
 x is divisible by 15 
 x is NOT divisible by 20  
 Step 1: Prime Factorization 
Let's look at the prime factorizations of the key numbers:
 
 15 = 3 × 5 
 20 = 22 × 5 
 6 = 2 × 3 
 10 = 2 × 5 
 12 = 22 × 3 
 30 = 2 × 3 × 5 
 150 = 2 × 3 × 52  
 Step 2: Analyze Divisibility by 15 
 
 Since x is divisible by 15, x MUST contain the prime factors 3 and 5 
 x = 3 × 5 × k, where k is some integer  
 Step 3: Incompatibility with 20 
 
 x is NOT divisible by 20 
 This means x cannot have both 22 and 5 as prime factors simultaneously 
 x CAN have a single 2, but no more than that  
 Step 4: Check Each Option 
 Option A: 6 (2 × 3) 
 
 x is guaranteed to have 3 as a factor 
 Possible divisibility by 6 ✓  
 Option B: 10 (2 × 5) 
 
 x has 5 as a factor 
 x has at most one 2 as a factor 
 Possible divisibility by 10 ✓  
 Option C: 12 (22 × 3) 
 
 x has 3 as a factor 
 x can only have at most one 2 
 NOT divisible by 12! ✗  
 Option D: 30 (2 × 3 × 5) 
 
 x has both 3 and 5 as factors 
 Possible divisibility by 30 ✓  
 Option E: 150 (2 × 3 × 52) 
 
 x has both 3 and 5 as factors  
 Possible divisibility by 150 ✓

Hence,
The answer is  C. 12

If x is an integer divisible by 15 but not divisible by 20, then x

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If x is an integer divisible by 15 but not divisible by 20, then x

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