Last visit was: 12 Jul 2024, 17:03 It is currently 12 Jul 2024, 17:03
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 395
Own Kudos [?]: 16999 [8]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
User avatar
Intern
Intern
Joined: 29 Jun 2011
Posts: 8
Own Kudos [?]: 17 [0]
Given Kudos: 0
Location: Ireland
Concentration: (trading as) Test Prep Dublin
 Q50  V40
Send PM
User avatar
Manager
Manager
Joined: 11 Apr 2011
Posts: 58
Own Kudos [?]: 70 [0]
Given Kudos: 16
Send PM
avatar
Intern
Intern
Joined: 08 Mar 2014
Posts: 5
Own Kudos [?]: 2 [0]
Given Kudos: 3
Concentration: Finance, General Management
GPA: 3.12
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
enigma123 wrote:
If 90/k is an integer, is k an integer?

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?


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
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640179 [1]
Given Kudos: 84576
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
1
Kudos
Expert Reply
wikdwik wrote:
enigma123 wrote:
If 90/k is an integer, is k an integer?

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?


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


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.
User avatar
Intern
Intern
Joined: 21 Jun 2014
Posts: 21
Own Kudos [?]: 114 [0]
Given Kudos: 184
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
Bunuel wrote:
wikdwik wrote:
enigma123 wrote:
If 90/k is an integer, is k an integer?

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?


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


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.


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
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640179 [0]
Given Kudos: 84576
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
Expert Reply
sandeepmanocha wrote:
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


I tried to understand what you've written there but failed...
User avatar
Manager
Manager
Joined: 18 Mar 2014
Posts: 205
Own Kudos [?]: 139 [0]
Given Kudos: 175
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE:Information Technology (Computer Software)
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
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
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640179 [1]
Given Kudos: 84576
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
1
Kudos
Expert Reply
adityadon wrote:
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


Question asks: is k an integer?

(2 ) says that k is a multiple of a prime number, which means that k IS an integer.
User avatar
Intern
Intern
Joined: 21 Jun 2014
Posts: 21
Own Kudos [?]: 114 [0]
Given Kudos: 184
Send PM
If 90/k is an integer, is k an integer? [#permalink]
Sorry for the confusion - I will try to elaborate now with examples -

Bunuel wrote:
sandeepmanocha wrote:
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


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



You said
Quote:
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. ab=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.


But there is Another Possibility, like one given below

wikdwik wrote:

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 ?


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)
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640179 [1]
Given Kudos: 84576
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
1
Kudos
Expert Reply
sandeepmanocha wrote:
Sorry for the confusion - I will try to elaborate now with examples -

Bunuel wrote:
sandeepmanocha wrote:
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


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



You said
Quote:
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. ab=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.


But there is Another Possibility, like one given below

wikdwik wrote:

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 ?


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)


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.
User avatar
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 393 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
If 90/k is an integer, is k an integer? [#permalink]
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

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

[2] 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.
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30788 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
Expert Reply
Top Contributor
enigma123 wrote:
If 90/k is an integer, is k an integer?

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


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
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33952
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: If 90/k is an integer, is k an integer? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If 90/k is an integer, is k an integer? [#permalink]
Moderator:
Math Expert
94302 posts