Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

Each of A, B and C represents a one-digit integer. AB and BA

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Each of A, B and C represents a one-digit integer. AB and BA

by Max@Math Revolution » Wed May 15, 2019 11:28 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

Each of A, B and C represents a one-digit integer. AB and BA are two-digit integers, and CAA is a three-digit integer. If BA + AB + AB = CAA, what is the value of A?

A. 1
B. 2
C. 3
D. 4
E. 5
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu May 16, 2019 2:16 am
Max@Math Revolution wrote:[GMAT math practice question]

Each of A, B and C represents a one-digit integer. AB and BA are two-digit integers, and CAA is a three-digit integer. If BA + AB + AB = CAA, what is the value of A?

A. 1
B. 2
C. 3
D. 4
E. 5
325 = 100*3 + 10*2 + 5
648 = 100*6 + 10*4 + 8
Generally:
Three-digit integer XYZ = 100X + 10Y + Z

Since BA + AB + AB = CAA, we get:
(10B+A) + (10A+B) + (10A+B) = 100C + 10A + A
12B + 21A = 100C + 11A
12B + 10A = 100C
12B + 10A = MULTIPLE OF 100
Since B and A are digits, the left side will yield a multiple of 100 only if B=5 and A=4, with the result that 12B+10A = (12*5) + (10*4) = 100.
Thus, A=4.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Sun May 19, 2019 4:56 pm
=>

Equating the units digits of BA + AB + AB and CAA gives either A + B + B = A or A + B + B = 10 + A. So, B = 5 or B = 0.
Since BA is a two-digit integer, we must have B = 5.
After carrying from the addition of the units digits, adding the tens digits yields B + A + A + 1 = 5 + A + A + 1 = 10 + A or A = 4.

Therefore, the answer is D.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1