• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

What is the value of A?

This topic has 3 expert replies and 0 member replies

GMAT/MBA Expert

What is the value of A?

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



[Math Revolution GMAT math practice question]

What is the value of A?

1) The four-digit number A77A is a multiple of 4.
2) The four-digit number A77A is a multiple of 9.

_________________

Math Revolution
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 $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the value of A?

1) The four-digit number A77A is a multiple of 4.
2) The four-digit number A77A is a multiple of 9.
$$? = A\,\,\,\,\left( {\,A \in \left\{ {1,2,3, \ldots ,9} \right\}\,\,:\,\,{\rm{already}}\,\,{\rm{considering}}\,\,{\rm{each}}\,\,{\rm{statement}}\,\,{\rm{alone}}\,} \right)$$
$$\left( 1 \right)\,\,\,{{\left\langle {A77A} \right\rangle } \over 4} = {\mathop{\rm int}} \,\,\,\,\, \Leftrightarrow \,\,\,\,{{\left\langle {7A} \right\rangle } \over 4} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,A = 2\,\,\,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,A = 6\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\,{{\left\langle {A77A} \right\rangle } \over 9} = {\mathop{\rm int}} \,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,{{2 \cdot A + 14} \over 9} = {\mathop{\rm int}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,A = 2\,\,\,\,\,\,\left( {\,9 \cdot k = 14 + 2 \cdot A\,\,,\,\,k > 2\,\,\,\, \Rightarrow \,\,\,\,A > 9} \right)$$

The correct answer is therefore (B).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the value of A?

1) The four-digit number A77A is a multiple of 4.
2) The four-digit number A77A is a multiple of 9.
The four-digit number A77A is a multiple of 4

Since A77A is a multiple of 4, 7A must be a multiple of 4, so we see that 7A could be either 76 or 72. Thus, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The four-digit number A77A is a multiple of 9.

We see that 2A + 7 + 7 = 2A + 14 must be a multiple of 9; thus, A must be 2. Statement two alone is sufficient to answer the question.

Answer: B

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2219 messages
Followed by:
32 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

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.

Since we have 1 variable (A) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If the last two digit is a multiple of 4, the original number is a multiple of 4.
Thus, A is 2 or 6 since 72 and 76 are multiples of 4.
Condition 1) is not sufficient, because we don’t have a unique answer

Condition 2)
If the sum of all digits is a multiple of 9, the original number is a multiple of 9.
A + 7 + 7 + A = 2A + 14
If 2A + 14 = 18, we have 2A = 4 or A = 2.
We don’t have any digit integer A such that 2A = 9, 27 or 36.
Thus A = 2 is the unique integer.
Condition 2) is sufficient.

Answer: C

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.

_________________

Math Revolution
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 $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Top First Responders*

1 Jay@ManhattanReview 67 first replies
2 Brent@GMATPrepNow 64 first replies
3 GMATGuruNY 44 first replies
4 Ian Stewart 23 first replies
5 Scott@TargetTestPrep 17 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

211 posts
2 image description Max@Math Revolution

Math Revolution

94 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
4 image description GMATGuruNY

The Princeton Review Teacher

69 posts
5 image description Jay@ManhattanReview

Manhattan Review

68 posts
See More Top Beat The GMAT Experts