GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Jun 2019, 08:25

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

If a number N is decreased by p percent and then the resulting value

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
G
Joined: 27 Aug 2014
Posts: 149
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)
CAT Tests
If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 01 Oct 2015, 06:32
1
24
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:30) correct 69% (02:55) wrong based on 325 sessions

HideShow timer Statistics

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.
Manager
Manager
avatar
Joined: 06 Mar 2014
Posts: 89
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 16 Nov 2015, 04:40
Harley1980:

Can you provide some insight on this one.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 16 Nov 2015, 11:06
1
2
santorasantu wrote:
If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


N decreased by p Percent

i.e. N becomes-----> N*[1-(p/100)]

Resulting value increased by q Percent

i.e. N*[1-(p/100)] becomes-----> N*[1-(p/100)]*[1+(q/100)]

Now, N*[1-(p/100)]*[1+(q/100)] = N

i.e. (100-p)*(100+q) = 100*100 = \(2^4*5^4\)

Statement 1: p is not a multiple of 10.
Case 1: p = 75 and q = 300
Case 2: p = 95 and q = 1900
NOT SUFFICIENT

Statement 2: q is not a multiple of 10.
Case 1: q = 25 and p = 20
Case 2: q = 525 and p = 84
NOT SUFFICIENT

Combining the two statements
Only possible values are
q = 525 and p = 84
SUFFICIENT
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
SVP
SVP
User avatar
V
Joined: 26 Mar 2013
Posts: 2231
Reviews Badge CAT Tests
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 Nov 2015, 01:51
Hi GMATinsight,

When combined 1 & 2, I found difficult to get the answer and in the real test it will be waste of time. Do you have any short cut to know there is only one unique answer such that the answer will be C?

Thanks
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 Nov 2015, 09:36
1
1
Mo2men wrote:
Hi GMATinsight,

When combined 1 & 2, I found difficult to get the answer and in the real test it will be waste of time. Do you have any short cut to know there is only one unique answer such that the answer will be C?

Thanks


i.e. (100-p)*(100+q) = 100*100 = \(2^4∗5^4\)

Combining the two statements
Since and p and q are both NON-MULTIPLE of 10 so (100-p) and (100+q) also will be NON-MULTIPLE of 10

i.e. the values of (100-p) and (100+q) will include either powers of only 2 (i.e. 2 or 2^2 or 2^3 or 2^4) or powers of only 5 (i.e. 5 or 5^2 or 5^3 or 5^4)

Also, Note that p can NOT be greater than 100 because (100-p) must be POSITIVE

Only possible values of p are
q = 525 and p = 84
(100-p)*(100+q) = 16*625 = 100*100
SUFFICIENT

I Hope this helps!!!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 Nov 2015, 10:38
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 237
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 Nov 2015, 10:56
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.



how would one think of such possible answers during the test? what level hardness question is this?
Manager
Manager
avatar
B
Joined: 09 Oct 2015
Posts: 237
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 Nov 2015, 11:00
GMATinsight wrote:
Mo2men wrote:
Hi GMATinsight,

When combined 1 & 2, I found difficult to get the answer and in the real test it will be waste of time. Do you have any short cut to know there is only one unique answer such that the answer will be C?

Thanks


i.e. (100-p)*(100+q) = 100*100 = \(2^4∗5^4\)

Combining the two statements
Since and p and q are both NON-MULTIPLE of 10 so (100-p) and (100+q) also will be NON-MULTIPLE of 10

i.e. the values of (100-p) and (100+q) will include either powers of only 2 (i.e. 2 or 2^2 or 2^3 or 2^4) or powers of only 5 (i.e. 5 or 5^2 or 5^3 or 5^4)

Also, Note that p can NOT be greater than 100 because (100-p) must be POSITIVE

Only possible values of p are
q = 525 and p = 84
(100-p)*(100+q) = 16*625 = 100*100
SUFFICIENT

I Hope this helps!!!



on simplifying using another method, i arrive at
100(q-p) = pq

any help from here?
Intern
Intern
avatar
Joined: 01 Mar 2016
Posts: 6
GMAT ToolKit User
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 17 May 2016, 14:13
GMATinsight wrote:
santorasantu wrote:

Now, N*[1-(p/100)]*[1+(q/100)] = N

i.e. (100-p)*(100+q) = 100*100 = \(2^4*5^4\)




I cannot find an algebraic way to arrive at this equation. How is this determined?
I can get to { [1-(p/100)]*[1+(q/100)] = 1 }.
However, when multiplying both sides by 100, I get { (100-p)*(100+q) = 100 }..
VP
VP
User avatar
D
Joined: 23 Feb 2015
Posts: 1031
GMAT 1: 720 Q49 V40
GMAT 2: 760 Q50 V42
GMAT ToolKit User Premium Member
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 06 Dec 2016, 13:47
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).

The original question stem says:
N*(100-p / 100)*(100+q / 100) = N
can we really divide the equation by N?
There is no indication in the question that ''N is not zero''. So, why do we divide the equation by N?
Thanks...
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Henry Wadsworth Longfellow

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 13 Dec 2016, 04:51
iMyself wrote:
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).

The original question stem says:
N*(100-p / 100)*(100+q / 100) = N
can we really divide the equation by N?
There is no indication in the question that ''N is not zero''. So, why do we divide the equation by N?
Thanks...


Hi iMyself,

Because there is a condition that n is not 0.

Happy Studying!
Math Revolution
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
VP
VP
User avatar
D
Joined: 23 Feb 2015
Posts: 1031
GMAT 1: 720 Q49 V40
GMAT 2: 760 Q50 V42
GMAT ToolKit User Premium Member
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 19 Dec 2016, 13:06
MathRevolution wrote:
iMyself wrote:
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?

(1) p is not a multiple of 10.

(2) q is not a multiple of 10.


If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).

The original question stem says:
N*(100-p / 100)*(100+q / 100) = N
can we really divide the equation by N?
There is no indication in the question that ''N is not zero''. So, why do we divide the equation by N?
Thanks...


Hi iMyself,

Because there is a condition that n is not 0.

Happy Studying!
Math Revolution

The question stem did not directly say that N is not 0, but it indirectly indicates that N is not zero by stating the line ''a number N is decreased by p percent.......''. If a number is decreased by a certain percent, then it indicates that N must be greater than zero, right MathRevolution? Thank you for your kind response.
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Henry Wadsworth Longfellow

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Intern
Intern
avatar
Joined: 17 Oct 2014
Posts: 5
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 28 Dec 2016, 12:48
how did you come up two values for p&q that is 84 and 525 please explain
Intern
Intern
avatar
B
Joined: 17 Aug 2016
Posts: 48
If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 01 Jan 2017, 08:41
Even if pretty loose the way I solved it is the following:

Once we arrive to (100-p)*(100+q) = 100*100 = 2^4∗5^4 we know the factorisation of (100-p)*(100+q)

Stm 1 tells us p is not a multiple of 10, therefore 100-p is not a multiple of 10 either. Thus 100-p contains only 2s or 5s in its factorisation, but we don't know in which quantity. i.e. 100-p can be 2^3 (p is 92) or 5^2 (p is 75). The rest of the factorisation of (100-p)*(100+q) will be covered by 100+q as long as this factorisation yields a number >100 --> No suff.

Stm 2 same as above but with different constraints. This time 100+q contains only 2s or only 5s. The limit here is that 100-p cannot be >100. --> No suff.

Stm 1 and 2 clearly here we know that either (100-p) contains only 2s or it contains only 5s (vice versa for (100+q))
Since (100-p) cannot be >100 (100-p) is 2^4 (p=84) and (100+q) is 5^4 (q=525) ---> C is the answer
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 11 Jan 2017, 01:13
1
2
Hi iMyself,

Condition 1)

N * ( 1 - p/100 ) ( 1 + q / 100 ) = N
( 1 - p / 100 ) ( 1 + q / 100 ) = 1
( 100 - p ) ( 100 + q ) = 10,000 = 2^4 * 5^4

We have two cases satisfying the first condition.

case 1: 100 - p = 2^4, 100 + q = 5^4
100 - p = 16, 100 + q = 625
p = 84, q = 525

case 2: 100 - p = 5^2, 100 + q = 2^4 * 5^2
100 - p = 25, 100 + q = 400
p = 75, q = 300

Not Sufficient


Condition 2)

case 1: 100 - p = 2^4, 100 + q = 5^4
p = 84, q = 525

case 2: 100 - p = 2^4 * 5, 100 + q = 5^3
100 - p = 80, 100 + q = 125
p = 20, q = 25

Not Sufficient


Considering both conditions together, the only case for them is 100 - p = 2^4 and 100 + q = 5^4., since prime factors 2 and 5 cannot be together in 100 - p or 100 + q and p must be less than or equal to 100.
Then 100 - p = 16 and 100 + q = 625

p = 84 and q = 525 is the unique solution

The correct answer is C.

Happy Studying!
Math Revolution
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
S
Joined: 10 May 2018
Posts: 50
Location: Argentina
GMAT 1: 680 Q48 V35
Re: If a number N is decreased by p percent and then the resulting value  [#permalink]

Show Tags

New post 14 Sep 2018, 08:34
mattyahn wrote:
GMATinsight wrote:
santorasantu wrote:

Now, N*[1-(p/100)]*[1+(q/100)] = N

i.e. (100-p)*(100+q) = 100*100 = \(2^4*5^4\)




I cannot find an algebraic way to arrive at this equation. How is this determined?
I can get to { [1-(p/100)]*[1+(q/100)] = 1 }.
However, when multiplying both sides by 100, I get { (100-p)*(100+q) = 100 }..


I believe this should not be multiplied by 100 in both sides because multiplication is not distributive. I believe you would get (100-p)*(1+q/100)=100. and hence you would need another 100 to multiply.

I was having the same issue...hope this helps.
GMAT Club Bot
Re: If a number N is decreased by p percent and then the resulting value   [#permalink] 14 Sep 2018, 08:34
Display posts from previous: Sort by

If a number N is decreased by p percent and then the resulting value

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne