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# If a, b, and c are consecutive 2-digit positive integers in that order

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If a, b, and c are consecutive 2-digit positive integers in that order  [#permalink]

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09 Aug 2018, 01:30
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65% (hard)

Question Stats:

63% (02:52) correct 38% (02:10) wrong based on 56 sessions

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[Math Revolution GMAT math practice question]

If $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in that order, and $$a+b+c$$ is a multiple of $$10$$, what is the value of $$c$$?

1) $$a$$ is a prime number
2) $$c$$ is a prime number

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Status: Learning stage Joined: 01 Oct 2017 Posts: 1014 WE: Supply Chain Management (Energy and Utilities) If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 01:51 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in that order, and $$a+b+c$$ is a multiple of $$10$$, what is the value of $$c$$? 1) $$a$$ is a prime number 2) $$c$$ is a prime number Let a=x-1, b=x, and c=x+1 where x>10 and an an integer. So, a+b+c=3x=10k (Given) So, $$x=(\frac{10}{3})*k$$ We have (a,b,c) triplets when k=6,9,12,15,....27. So we have (a,b,c)=(19,20,21), (29,30,31),.............,(59,60,61),.....,(89,91,90) St1:-$$a$$ is a prime number. c could be 21,31 etc Insufficient. St2:- $$c$$ is a prime number c could be 31,41,61. Insufficient. Combined, we have two pair of triplets, (29,30,31) and (59,60,61), where c has two values. Insufficient. Ans. (E) _________________ Regards, PKN Rise above the storm, you will find the sunshine SVP Joined: 26 Mar 2013 Posts: 2345 If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 02:50 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in that order, and $$a+b+c$$ is a multiple of $$10$$, what is the value of $$c$$? 1) $$a$$ is a prime number 2) $$c$$ is a prime number $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in order could be as follows a,a+1,a+2...........So a+a+1+a+2 = 3a+3= 3(a+1) = mulitple of 10....this will happen if a =19 or 29 or 39.............89..the question will be: Is a =19 or 29 or 39..........or 89?? Note it can't be 99 as b and c will be 3 digit numbers. 1) $$a$$ is a prime number Many values for a. It could be 19 or 29 or 59 or 79 Insufficent 2) $$c$$ is a prime number Many values for c. If a =29.... then c= 31= prime If a =59......then c=61= Prime Combine 1 & 2 Take same examples above.............No clear value for a Answer: E VP Joined: 09 Mar 2016 Posts: 1230 Re: If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 08:52 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in that order, and $$a+b+c$$ is a multiple of $$10$$, what is the value of $$c$$? 1) $$a$$ is a prime number 2) $$c$$ is a prime number ST 1. 41 40 39 ST 2. 39 40 41 so C could be any value. hence E can someone confirm if my understanding is correct Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 19:12 1 dave13 wrote: MathRevolution wrote: [Math Revolution GMAT math practice question] If $$a, b,$$ and $$c$$ are consecutive 2-digit positive integers in that order, and $$a+b+c$$ is a multiple of $$10$$, what is the value of $$c$$? 1) $$a$$ is a prime number 2) $$c$$ is a prime number ST 1. 41 40 39 ST 2. 39 40 41 so C could be any value. hence E can someone confirm if my understanding is correct dave13 , Yes C Can be any value when you combine both Statement 1 & 2 Ex: (29,30,31) and (59,60,61) 39 40 41 Doesn't hold ture, when you combine both Statements bcoz 39 is not a Prime _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8009 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 13 Aug 2018, 06:21 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since a = b – 1 and c = b + 1, we have a + b + c = ( b – 1 ) + b + ( b + 1 ) = 3b is a multiple of 10 and b is a multiple of 10. Thus, the possible triples ( a, b, c ) are ( 19, 20, 21 ), ( 29, 30, 31 ), ( 39, 40, 41 ), ( 49, 50, 51 ), ( 59, 60, 61 ), ( 69, 70, 71 ), ( 79, 80, 81 ) and ( 89, 90, 91 ). Since we have 3 variables and 2 equations ( a = b – 1, c = b + 1), D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) The triples in which a is a prime number are ( 19, 20, 21 ), ( 29, 30, 31 ), ( 59, 60, 61 ), ( 79, 80, 81 ) and ( 89, 90, 91 ). Thus, c could be 21, 31, 61, 81 or 91. Since we don’t have a unique solution, condition 1) is not sufficient. Condition 2) The triples in which c is a prime number are ( 29, 30, 31 ), ( 39, 40, 41 ), ( 59, 60, 61 ), ( 69, 70, 71 ) and ( 89, 90, 91 ). Thus, c could be 31, 41, 61, 71 or 91. Since we don’t have a unique solution, condition 2) is not sufficient. Conditions 1) & 2): The triples in which both a and c are prime numbers are: ( 29, 30, 31 ), ( 59, 60, 61 ) and ( 89, 90, 91 ). Thus, c could be 31, 61 or 91. Since we don’t have a unique solution, both conditions are not sufficient, when considered together. Therefore, E is the answer. Answer: E If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but 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$79 for 1 month Online Course"
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Re: If a, b, and c are consecutive 2-digit positive integers in that order  [#permalink]

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04 Sep 2019, 11:58
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Re: If a, b, and c are consecutive 2-digit positive integers in that order   [#permalink] 04 Sep 2019, 11:58
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