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

 It is currently 19 Aug 2018, 03:11

### 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

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

# What is the value of p + q + r

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
What is the value of p + q + r  [#permalink]

### Show Tags

Updated on: 09 Aug 2018, 08:31
5
00:00

Difficulty:

(N/A)

Question Stats:

38% (02:04) correct 62% (02:08) wrong based on 121 sessions

### HideShow timer Statistics

What is the value of p + q + r, where p, q, r are positive integers?

(1) $$7p × 5q = 175$$ and $$4p = r$$

(2) $$r$$ is 200% more than $$p$$ and 100% more than $$q$$, where $$p + r$$ is a single digit number.

Originally posted by gsingh0711 on 05 Aug 2018, 09:46.
Last edited by amanvermagmat on 09 Aug 2018, 08:31, edited 2 times in total.
Edited the OA
Manager
Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: What is the value of p + q + r  [#permalink]

### Show Tags

Updated on: 08 Aug 2018, 19:51
3
1
Explanation:

Given p, q, r are positive (hence non-zero) integers. And we need to find the value of p + q + r.

Considering statement 1:
7p × 5q = 175 and 4p = r
7p × 5q = (7*1)*(5*5)
⇒ p = 1 and q = 5
and r = 4(1) = 4

⇒ p + q + r = 10

Since we are getting a definite answer from above statement, statement 1 itself is sufficient to provide the answer.

Considering statement 2:
r is 200% more than p and 100% more than q, where p + r is a single digit number

⇒ r = p + 200p/100 = 3p
and r = q + 100q/100 = 2q

⇒ p + r = p + 3p = 4p
Now, 4p is either 4 or 8
⇒ p = 1 or 2
Hence, r = 3p = 3 or 6

And r = 2q gives: q = 1.5 or 3. However, since these are positive integers, q = 3 (p cannot be 1).
⇒ p + q + r = 2 + 6 + 3 = 11

Since we are getting a definite answer from above statement, statement 2 itself is sufficient to provide the answer.

As statement 1 and 2 both alone are sufficient to provide the answer.

I think, I deserve a kudus LOL

Originally posted by gsingh0711 on 05 Aug 2018, 09:47.
Last edited by gsingh0711 on 08 Aug 2018, 19:51, edited 1 time in total.
Intern
Joined: 21 May 2017
Posts: 42
Re: What is the value of p + q + r  [#permalink]

### Show Tags

05 Aug 2018, 10:13
1
gsingh0711 wrote:
Explanation:

Given p, q, r are positive (hence non-zero) integers. And we need to find the value of p + q + r.

Considering statement 1:
7p × 5q = 175 and 4p = r
7p × 5q = 52 × 7
⇒ p = 1 and q = 2
and r = 4(1) = 4

⇒ p + q + r = 7

Since we are getting a definite answer from above statement, statement 1 itself is sufficient to provide the answer.

Considering statement 2:
r is 200% more than p and 100% more than q, where p + r is a single digit number

⇒ r = p + 200p/100 = 3p
and r = q + 100q/100 = 2q

⇒ p + r = p + 3p = 4p
Now, 4p is either 4 or 8
⇒ p = 1 or 2
Hence, r = 3p = 3 or 6

And r = 2q gives: q = 1.5 or 3. However, since these are positive integers, q = 3 (p cannot be 1).
⇒ p + q + r = 2 + 6 + 3 = 11

Since we are getting a definite answer from above statement, statement 2 itself is sufficient to provide the answer.

As statement 1 and 2 both alone are sufficient to provide the answer.

I think, I deserve a kudus LOL
You mistyped 25 as 52.
Also, I don't think Statement1 is sufficient.

7p*5q = 175
p*q = 5
p = 1 or 5
q = 5 or 1

r = 4p = 4 or 20

All of this makes Statement1 insufficient.

One way to make sure that your answer is right is to match the (p+q+r) values you get from each statement. They have to be equal.

On a side note, this question seems odd.
Statement1 says r=4p and
Statement2 says r=3p

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Senior Manager
Joined: 15 Oct 2017
Posts: 278
Re: What is the value of p + q + r  [#permalink]

### Show Tags

05 Aug 2018, 14:23
Statement 1 does not seem sufficient. Kindly post the source of the question. In my opinion, answer should be B.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of p + q + r  [#permalink]

### Show Tags

06 Aug 2018, 01:46
urvashis09 wrote:
Statement 1 does not seem sufficient. Kindly post the source of the question. In my opinion, answer should be B.

I think you are correct.

St1:- 2 pairs of triplets(p,q,r), viz, (1,5,4) and (5,1,20).
So two values of p+q+r.
Therefore, insufficient.

St2:- Only one pair of triplets(p,q,r), i.e, (2,6,3)
So an unique value of p+q+r.
Therefore, sufficient.

Ans. (B)

P.S:- gsingh0711, request to provide official explanation along with source of the question.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 12 Mar 2018
Posts: 7
Re: What is the value of p + q + r  [#permalink]

### Show Tags

08 Aug 2018, 10:52
Statement 1:
7p*5q = 175
p*q =$$\frac{175}{35}$$
p*q = 5.

Thus p can be 1 or 5, or q can be 1 or 5.
we know 4p = r.
therefore substitute p = r/4 in pq =5 we also get rq = 20

if p =1 then r =4 q =5 then rq =20
but if p=5 , r=20, q=1 rq is still 20.
thus 1+4+5 = 10 Statement one is not sufficient.

Meanwhile Statement 2 is very much sufficient
as mentioned by other comments. I don't see what I missed
Manager
Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: What is the value of p + q + r  [#permalink]

### Show Tags

08 Aug 2018, 14:55
PKN wrote:
urvashis09 wrote:
Statement 1 does not seem sufficient. Kindly post the source of the question. In my opinion, answer should be B.

I think you are correct.

St1:- 2 pairs of triplets(p,q,r), viz, (1,5,4) and (5,1,20).
So two values of p+q+r.
Therefore, insufficient.

St2:- Only one pair of triplets(p,q,r), i.e, (2,6,3)
So an unique value of p+q+r.
Therefore, sufficient.

Ans. (B)

P.S:- gsingh0711, request to provide official explanation along with source of the question.

Official explanation has already been provided. source of the question is tagged as Other.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of p + q + r  [#permalink]

### Show Tags

08 Aug 2018, 19:19
gsingh0711 wrote:
PKN wrote:
urvashis09 wrote:
Statement 1 does not seem sufficient. Kindly post the source of the question. In my opinion, answer should be B.

I think you are correct.

St1:- 2 pairs of triplets(p,q,r), viz, (1,5,4) and (5,1,20).
So two values of p+q+r.
Therefore, insufficient.

St2:- Only one pair of triplets(p,q,r), i.e, (2,6,3)
So an unique value of p+q+r.
Therefore, sufficient.

Ans. (B)

P.S:- gsingh0711, request to provide official explanation along with source of the question.

Official explanation has already been provided. source of the question is tagged as Other.

Thank you gsingh0711,
Noted. I don't agree with the official explanation provided by you.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Manager
Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: What is the value of p + q + r  [#permalink]

### Show Tags

08 Aug 2018, 19:54
PKN

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of p + q + r  [#permalink]

### Show Tags

08 Aug 2018, 20:07
gsingh0711 wrote:
PKN

Hi gsingh0711,

I have already shared my approach under the same post. Kindly review and correct me.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 03 Apr 2012
Posts: 13
GMAT 1: 640 Q43 V34
Re: What is the value of p + q + r  [#permalink]

### Show Tags

09 Aug 2018, 05:14
Statement1:-

7p*5q=175 -> p*q=5=> p=5 or 1 and q=1 or 5
4*p=r -> r can be 4*1=4 or 4*5=20
So, either (p,q,r)= (1,5,4) or (5,1,20).
p+q+r= 10 or 26
Therefore, insufficient.

Statement2:- r is 200% more than p -> r=3p &

and 100% more than q -> r=2q -> r=3p=2q

(p,q,r)= (1,2,3) or (2,4,6) ................p+r ( 4 or 8)- is a single digit number.

p+q+r= 6 or 12
Therefore, insufficient.

combining both statements also do not result in to a single triplet.

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of p + q + r  [#permalink]

### Show Tags

09 Aug 2018, 05:27
rajkumarchinthala wrote:
Statement1:-

7p*5q=175 -> p*q=5=> p=5 or 1 and q=1 or 5
4*p=r -> r can be 4*1=4 or 4*5=20
So, either (p,q,r)= (1,5,4) or (5,1,20).
p+q+r= 10 or 26
Therefore, insufficient.

Statement2:- r is 200% more than p -> r=3p &

and 100% more than q -> r=2q -> r=3p=2q

(p,q,r)= (1,2,3) or (2,4,6) ................p+r ( 4 or 8)- is a single digit number.

p+q+r= 6 or 12
Therefore, insufficient.

combining both statements also do not result in to a single triplet.

Hi rajkumarchinthala,

(p,q,r)=(1,2,3) or (2,4,6) seems incorrect since it fails to qualify the conditions given in st2.
r=3p=2q.

The only possible triplet is (2,3,6), where p=2, q=3, and r=3p=3*2=6=2*q=2*3=6.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Joined: 03 Apr 2012
Posts: 13
GMAT 1: 640 Q43 V34
Re: What is the value of p + q + r  [#permalink]

### Show Tags

09 Aug 2018, 05:33
PKN wrote:
rajkumarchinthala wrote:
Statement1:-

7p*5q=175 -> p*q=5=> p=5 or 1 and q=1 or 5
4*p=r -> r can be 4*1=4 or 4*5=20
So, either (p,q,r)= (1,5,4) or (5,1,20).
p+q+r= 10 or 26
Therefore, insufficient.

Statement2:- r is 200% more than p -> r=3p &

and 100% more than q -> r=2q -> r=3p=2q

(p,q,r)= (1,2,3) or (2,4,6) ................p+r ( 4 or 8)- is a single digit number.

p+q+r= 6 or 12
Therefore, insufficient.

combining both statements also do not result in to a single triplet.

Hi rajkumarchinthala,

(p,q,r)=(1,2,3) or (2,4,6) seems incorrect since it fails to qualify the conditions given in st2.
r=3p=2q.

The only possible triplet is (2,3,6), where p=2, q=3, and r=3p=3*2=6=2*q=2*3=6.

------------------------------

Thanks. Missed out on that.

B is the answer. However, the answer here is showing as D.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
Re: What is the value of p + q + r  [#permalink]

### Show Tags

09 Aug 2018, 05:39
rajkumarchinthala wrote:
PKN wrote:
rajkumarchinthala wrote:
Statement1:-

7p*5q=175 -> p*q=5=> p=5 or 1 and q=1 or 5
4*p=r -> r can be 4*1=4 or 4*5=20
So, either (p,q,r)= (1,5,4) or (5,1,20).
p+q+r= 10 or 26
Therefore, insufficient.

Statement2:- r is 200% more than p -> r=3p &

and 100% more than q -> r=2q -> r=3p=2q

(p,q,r)= (1,2,3) or (2,4,6) ................p+r ( 4 or 8)- is a single digit number.

p+q+r= 6 or 12
Therefore, insufficient.

combining both statements also do not result in to a single triplet.

Hi rajkumarchinthala,

(p,q,r)=(1,2,3) or (2,4,6) seems incorrect since it fails to qualify the conditions given in st2.
r=3p=2q.

The only possible triplet is (2,3,6), where p=2, q=3, and r=3p=3*2=6=2*q=2*3=6.

------------------------------

Thanks. Missed out on that.

B is the answer. However, the answer here is showing as D.

You are Welcome rajkumarchinthala,

Yeah you are correct, answer should be 'B'. But I am not sure why it appears 'D' under spoiler OA.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 507
WE: Supply Chain Management (Energy and Utilities)
What is the value of p + q + r  [#permalink]

### Show Tags

09 Aug 2018, 22:41
gsingh0711 wrote:
What is the value of p + q + r, where p, q, r are positive integers?

(1) $$7p × 5q = 175$$ and $$4p = r$$

(2) $$r$$ is 200% more than $$p$$ and 100% more than $$q$$, where $$p + r$$ is a single digit number.

Thanks a lot amanvermagmat for removing the incorrect spoiler OA with correct answer. No platform to award kudos.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

What is the value of p + q + r &nbs [#permalink] 09 Aug 2018, 22:41
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.