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What is the value of p + q + r

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What is the value of p + q + r  [#permalink]

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New post Updated on: 09 Aug 2018, 08:31
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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
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Re: What is the value of p + q + r  [#permalink]

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New post Updated on: 08 Aug 2018, 19:51
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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.

Answer: D.

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.
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Re: What is the value of p + q + r  [#permalink]

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New post 05 Aug 2018, 10:13
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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.

Answer: D.

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

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Re: What is the value of p + q + r  [#permalink]

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New post 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.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.
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Re: What is the value of p + q + r  [#permalink]

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New post 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
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Re: What is the value of p + q + r  [#permalink]

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New post 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.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.
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Re: What is the value of p + q + r  [#permalink]

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New post 08 Aug 2018, 19:54
PKN

Please review and share your feedback
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Re: What is the value of p + q + r  [#permalink]

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New post 08 Aug 2018, 20:07
gsingh0711 wrote:
PKN

Please review and share your feedback


Hi gsingh0711,

I have already shared my approach under the same post. Kindly review and correct me.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.

the answer is E.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.

the answer is E.


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.

Please check again.

The only possible triplet is (2,3,6), where p=2, q=3, and r=3p=3*2=6=2*q=2*3=6.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.

the answer is E.


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.

Please check again.

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.
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Re: What is the value of p + q + r  [#permalink]

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New post 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.

the answer is E.


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.

Please check again.

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.
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What is the value of p + q + r  [#permalink]

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New post 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. :-)
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What is the value of p + q + r &nbs [#permalink] 09 Aug 2018, 22:41
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