If 90/k is an integer, is k an integer?

Question

(1) k > 1
(2) k is a multiple of a prime number.

My approach:
 Considering Statement 1

k>1 so k can be an integer or could be in decimals i.e. 1.5. So insufficient

Considering Statement 2

K can be 2,3, 5, 9, --Therefore K has to be integer and sufficient.

Again is my concept and approach correct in answering this question?

testprepDublin · Answer

Your treatment of statement one is perfect but your treatment of statement two is a little complicated. The simple rule to remember here is that any multiple of a prime number has to be an integer.

pkmme · Answer

We dont need the additional 90/k = integer. B only is enough to prove

wikdwik · Answer

Statement 2 ->
K is a multiple of prime number = > 1.5 = 3 * .5 ( 3 is a prime no. K = 1.5 still holds)

Combining both statements still 1.5 holds and 3 holds true so E is the answer. Am I correct, what am I doing wrong ?

Regards,
wikdwik

Bunuel · Answer

On the GMAT when we are told that  a  is divisible by  b  (or which is the same: " a  is multiple of  b ", or " b  is a factor of  a "), we can say that: 
1.  a  is an integer;
2.  b  is an integer;
3.  \frac{a}{b}=integer .

So,  k is a multiple of prime number  means that k = prime*integer, which basically implies that k can be any integer but 1.

sandeepmanocha · Answer

When you say on the GMAT, does it means that it will not follow the general logic? And for Prime Numbers, can this be accepted as a TRUTH for Prime Numbers, that if any Number (N) is divided by any other INTEGER (K), which is also a Multiple of a Prime Number (All of them are), results in an INTEGER, this will imply that K will always be Integer?

:cry:

too much to remeber

too much to remeber

Bunuel · Answer

I tried to understand what you've written there but failed...

adityadon · Answer

clearly statement 1 not enough -

For statement 2 alone -
K is multiple of prime number means it could be - 
2 4 6 8 10 ...
3 6 9 12 15 ...
5 10 15 20 25 ...
7 14 21 ...

now if we factorize 90 = 3*3*5*2
so in short 3*3*5*2 / k should be integer.

if we start inserting values - for K as mulitple of 2 , 3*3*5*2/4 is not integer 
for K as multiple of 3 , 3*3*5*2/12 is not integer 
for k as multiple of 5 , 3*3*5*2/20 is not integer
for K as multiple of 7 and higher clearly its not integer ..

So both statement toghether not enough answer E
Where i m going wrong ???

Bunuel

Bunuel · Answer

Question asks: is k an integer?

(2 ) says that k is a multiple of a prime number, which means that k IS an integer.

sandeepmanocha · Answer

Sorry for the confusion - I will try to elaborate now with examples -

You said

But there is Another Possibility, like one given below

Now if I go by  wikdwik  my answer is E but if I go by your answer which is based on the concept "On the GMAT when we are told that a is divisible by...." then answer choice will be D

My question was - For the GMAT do we need to ALWAYS consider if the INTEGER (N) divided by any other NUMBER (K) = INTEGER, then K is also an INTEGER

Although following is also a possibility - 
N=90
K = 4.5 = 9 * .5 (Not INTEGER)
N/K = 20 (Integer)

Bunuel · Answer

Again, if k is NOT an integer it makes NO SENSE to say that k is a multiple of some integer.

If 90/k is an integer, is k an integer?

(1) k > 1. Not sufficient: k can be 2, so an integer or k can be 3/2, so not an integer.
 
(2) k is a multiple of a prime number. For k to be a multiple of an integer, it MUST be an integer, otherwise this statement won't have any sense. Sufficient.

Answer: B.

Hope it's clear.

pacifist85 · Answer

Hello, I worked on this one like this:

90 / k is an integer.
So, I tried t find the factors of 90, one of which should be k.

90....../.......Integer
90..................1
90..................2
45..................3
30..................4
x....................5
18..................6
15..................7
x....................8
x....................9
10.................10
9

is not sufficient as all of the factors apart of 1 are greater than 1.

is sufficient because if k is a multiple of a prime, taking primes and looking for their multiples we find that:
Taking 2, 2*15 = 30, k=30, 2*5=10, k = 10 etc. So, 90/k is an integer and k is an integer. Same in the cases below.
Taking 3, 3*10 = 30, k=30 etc
Taking 5, 5*2 = 10, k=10 etc
Taking 7, it gives none of the factors we found above, so it cannot be 7 (which we also see in the factor table above). Also, we know that 90/k is an integer, so this also rules out 7.
Taking 9, 9*10 = 90, k=90.

ANS is B

It looks long, but it actually took me 1.52 minute.

BrentGMATPrepNow · Answer

Given : 90/k is an integer

Target question :    Is k an integer?

Statement 1 : k > 1  
Let's TEST some values.
There are several values of k that satisfy statement 1. Here are two: 
 Case a : k = 10. Notice that 90/k = 90/10 = 9, which is an integer. In this case, the answer to the target question is  YES, k IS an integer 
 Case b : k = 90/77. Notice that 90/k = 90/(90/77) = 90(77/90) = 77, which is an integer. In this case, the answer to the target question is  NO, k is NOT an integer 
ince we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : k is a multiple of a prime number. 
All prime numbers are INTEGERS, and all multiples of integers are integers. 
 So, the answer to the target question is  YES, k IS an integer 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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If 90/k is an integer, is k an integer?

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