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What is the value of p + q + r
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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.
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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
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Updated on: 08 Aug 2018, 19:51
Explanation:
Given p, q, r are positive (hence nonzero) 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
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05 Aug 2018, 10:13
gsingh0711 wrote: Explanation:
Given p, q, r are positive (hence nonzero) 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 Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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Re: What is the value of p + q + r
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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
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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
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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
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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
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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
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08 Aug 2018, 19:54
PKNPlease review and share your feedback



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Re: What is the value of p + q + r
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08 Aug 2018, 20:07
gsingh0711 wrote: PKNPlease 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
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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
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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
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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
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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
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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
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