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

 It is currently 18 Dec 2018, 07:40

# Expecting Soon:

R1 Admission Decisions from McCombs - Join Chat Room for Latest Updates

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6661
GMAT 1: 760 Q51 V42
GPA: 3.82
If a, b, and c are consecutive 2-digit positive integers in that order  [#permalink]

### Show Tags

09 Aug 2018, 00:30
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:46) correct 36% (01:24) wrong based on 53 sessions

### HideShow timer Statistics

[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

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Status: Learning stage Joined: 01 Oct 2017 Posts: 931 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, 00:51 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: 1919 If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 01:50 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: 1251 Re: If a, b, and c are consecutive 2-digit positive integers in that order [#permalink] ### Show Tags 09 Aug 2018, 07:52 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: 531 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, 18:12 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: 6661 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, 05:21 => 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$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If a, b, and c are consecutive 2-digit positive integers in that order &nbs [#permalink] 13 Aug 2018, 05:21
Display posts from previous: Sort by