If k is a multiple of 24 but not a multiple of 16, which of the follow

Question

If k is a multiple of 24 but not a multiple of 16, which of the following cannot be an integer?

(A)  \frac{k}{8}

(B)  \frac{k}{9}

(C)  \frac{k}{32}

(D)  \frac{k}{36}

(E)  \frac{k}{81}

souvonik2k · Answer

k is a multiple of 24 but not a multiple of 16.
k=2x2x2x3xp
k is not equal to 2x2x2x2xq
A) Integer when k=24
B) Integer when k=72
C) Not an integer since each multiple of 32 will definitely be a multiple of 16
D) Integer when k=72
E) Integer when  k=2X2X2X3^4

Answer C.

PKN · Answer

We have  k=2^3*3^1*  (any odd integer) Let's check the options:-
A. k/8 is an integer when k=24*any odd integer
B. k/9 is an integer when k=24*3*any odd integer
C.  \frac{k}{32}   can never be an integer  . ( 32=2^5 , we can't make the odd integer= 2^2  since k is not a multiple of 16)
D.  36=2^2*3^2=2^3*3^1*\frac{3}{2}  , so k/36 is an integer.
E. 81=3^4=2^3*3^1*\frac{3^3}{2^3} , so k/36 is an integer.

Ans. (C)

JeffTargetTestPrep · Answer

If k is a multiple of 24, then k could be:

24, 48, 72, 96, 120, 144, …

However, since k is not a multiple of 16, then k can’t be:

48, 96, 144, …

So we see that k could only be:

24, 72, 120, …

That is, k is an odd multiple of 24.

We see that k/8 is an integer since 24 is divisible by 8. Furthermore, k/9 and k/81 could each be an integer if k is 9 x 24 and 81 x 24, respectively. Lastly, k/36 could be an integer if k is 9 x 24 (notice that 9 x 24 = 9 x 4 x 6 = 36 x 6). Therefore, k/32 can’t be integer (notice that 32 = 16 x 2, so if k is not a multiple of 16, then k can’t be a multiple of 32).

Answer: C

EgmatQuantExpert · Answer

Solution

Given:  
 • k is a multiple of 24 but not a multiple of 16

To find:  
 • The option which cannot be an integer.

Approach and Working:   
 • K is multiple of 24 then K can be written as  2^{(3+a)}*3^{(1+b)}* some other prime factors .
o However, k is not a multiple of 16.
o So, a must be 0.
• Thus, K=  2^3+*3^{(1+b)}* some other prime factors .

Now, among the given options, only  \frac{K}{32}  will not be an integer.

Hence, the correct answer is option C.

Answer: C  
 https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-NP-e1533292073470.jpg

101mba101 · Answer

We are given: k is a multiple of 24, k can be any of the following: 24, 48, 72, 96, 120, 144...

We are also told: k is not a multiple of 16. Thus, we can eliminate: 48, 96, 144...

We are left with values: 24, 72, 120...

On substituting in the values above in the given options, 24/32 , 72/32, 120/32 are not integers.

Thus, the answer is C.

Sabby · Answer

Hi,

If k is a multiple of 24 but not a multiple of 16, then k cannot be divided evenly by 16 or by a multiple of 16 
Looking at the options, only k/32 doesn't work as 32 is a multiple of 16.

Answer C)

ipsamdeleniti · Answer

32 is the only multiple of 16. Since k is not a multiple of 16, it can't be a multiple of 32, and so K/32 can't produce an integer.

If k is a multiple of 24 but not a multiple of 16, which of the follow

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If k is a multiple of 24 but not a multiple of 16, which of the follow

Prep Toolkit

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