A and B represent digits

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed May 02, 2012 4:33 am

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A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

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Source: Beat The GMAT — Problem Solving | Wed May 02, 2012 4:33 am

spartacus1412: Master | Next Rank: 500 Posts; Posts: 110; Joined: Wed Feb 22, 2012 11:28 pmFollowed by: 1 member; Location: India; Thanked: 13 times

by spartacus1412 » Wed May 02, 2012 6:14 am

Answer is 8

10A +B +B = 10B +A
a/b =8/9

Its do or die this time!
Practise, practise and practise.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed May 02, 2012 6:29 am

sanju09 wrote:A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

Alternatively, we can apply some logic here.
We can make 2 conclusions:

1) When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E.

2) When we add B+B, the sum is greater than 9.
We know this because we begin with a tens digit of A (as in AB) and once we add B, the sum becomes BA where the tens digit is now B.

Since we already know that the answer is B or D, we can just check each one.
This won't take long since we need only check one of these answer choices. If B works, we're done. If B doesn't work, the answer must be D.

Let's check answer choice B, which says A=6
If A = 6, then B must equal 8 (since 8+8=16)
If A=6 and B=8, we get: 68+8=86 (doesn't work, eliminate B)

So, the answer must be D

. . . Now, if we want to kill some time before the next question we could check this answer choice, but I'd just move on to the next question.

Let's check answer choice D (for the timid

)

Answer choice D says A=8
If A = 8, then B must equal 9 (since 9+9=18)
If A=8 and B=9, we get: 89+9=98 (WORKS!)

So, the answer is D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deojason: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jan 19, 2017 12:41 pm; Thanked: 1 times

by deojason » Thu Mar 23, 2017 1:20 pm

For some reason, this question is very confusing to me.

How did you come up with your first statement that "When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E."

I'm lost. Thanks!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Mar 23, 2017 1:29 pm

deojason wrote: How did you come up with your first statement that "When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E."

Let's examine some sums of two numbers that have the same units digit.
23 + 3 = 26
51 + 1 = 52
87 + 7 = 94
14 + 4 = 18

Notice that the units digit of the sum is equal to the units digit in the sum of two identical units digits.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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deojason: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Jan 19, 2017 12:41 pm; Thanked: 1 times

by deojason » Thu Mar 23, 2017 1:38 pm

Awesome! Thanks a lot! That makes sense now. I feel funny I didn't catch it the first time. I think it's time to rest since I've been watching your videos on Youtube, reading blogs, and answering practice questions for at least 5 hours now. LOL

Thanks a lot! You're a great help!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 10, 2018 7:59 am

sanju09 wrote:A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

We can apply some logic here.

We can make 2 conclusions:

1) When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E.

2) When we add B+B, the sum is greater than 9.
We know this because we begin with a tens digit of A (as in AB) and once we add B, the sum becomes BA where the tens digit is now B.

Since we already know that the answer is B or D, we can just check each one.
This won't take long since we need only check one of these answer choices. If B works, we're done. If B doesn't work, the answer must be D.

Let's check answer choice B, which says A=6
If A = 6, then B must equal 8 (since 8+8=16)
If A=6 and B=8, we get: 68+8=86 (doesn't work, eliminate B)

So, the answer must be D

. . . Now, if we want to kill some time before the next question we COULD check this answer choice, but I'd just move on to the next question.

Let's check answer choice D (for the timid!

)

Answer choice D says A=8
If A = 8, then B must equal 9 (since 9+9=18)
If A=8 and B=9, we get: 89+9=98 (WORKS!)

So, the answer is D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Jan 10, 2018 10:01 am

sanju09 wrote:A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

https://www.crushthetest.com

As written AB + B = BA representing digits.

So 10A + 2B = 10B + A

Rearranging, 9A - 8B = 0

So 9A= 8B. Pretty easy to see the LCM is 72

therefore A=8, D and B = 9

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Shamanthi: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Sep 24, 2018 6:07 am

by Shamanthi » Mon Sep 24, 2018 6:15 am

Brent@GMATPrepNow wrote:
sanju09 wrote:A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Alternatively, we can apply some logic here.
We can make 2 conclusions:

1) When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E.

2) When we add B+B, the sum is greater than 9.
We know this because we begin with a tens digit of A (as in AB) and once we add B, the sum becomes BA where the tens digit is now B.

Since we already know that the answer is B or D, we can just check each one.
This won't take long since we need only check one of these answer choices. If B works, we're done. If B doesn't work, the answer must be D.

Let's check answer choice B, which says A=6
If A = 6, then B must equal 8 (since 8+8=16)
If A=6 and B=8, we get: 68+8=86 (doesn't work, eliminate B)

So, the answer must be D

. . . Now, if we want to kill some time before the next question we could check this answer choice, but I'd just move on to the next question.

Let's check answer choice D (for the timid )

Answer choice D says A=8
If A = 8, then B must equal 9 (since 9+9=18)
If A=8 and B=9, we get: 89+9=98 (WORKS!)

So, the answer is D

Cheers,
Brent

Hi Brent,

I think there is a typo in the analysis of the answer B. 68+8= 76 (not 86) making it unsuitable for the answer.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 24, 2018 6:39 am

Shamanthi wrote:
Brent@GMATPrepNow wrote:
sanju09 wrote:A B
+ B
____
B A
____

In the correctly worked addition problem above, A and B represent digits. What is A?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Alternatively, we can apply some logic here.
We can make 2 conclusions:

1) When we add B+B the units digit of the sum is A
This means that A must be even. So, we can eliminate A, C and E.

2) When we add B+B, the sum is greater than 9.
We know this because we begin with a tens digit of A (as in AB) and once we add B, the sum becomes BA where the tens digit is now B.

Since we already know that the answer is B or D, we can just check each one.
This won't take long since we need only check one of these answer choices. If B works, we're done. If B doesn't work, the answer must be D.

Let's check answer choice B, which says A=6
If A = 6, then B must equal 8 (since 8+8=16)
If A=6 and B=8, we get: 68+8=86 (doesn't work, eliminate B)

So, the answer must be D

. . . Now, if we want to kill some time before the next question we could check this answer choice, but I'd just move on to the next question.

Let's check answer choice D (for the timid )

Answer choice D says A=8
If A = 8, then B must equal 9 (since 9+9=18)
If A=8 and B=9, we get: 89+9=98 (WORKS!)

So, the answer is D

Cheers,
Brent
Hi Brent,

I think there is a typo in the analysis of the answer B. 68+8= 76 (not 86) making it unsuitable for the answer.

I'm not saying that 68+8=86
I'm saying that, if A=6 and B=8, then our equation (AB + B = BA) becomes 68 + 8 = 86
Since this equation is faulty, we can eliminate answer choice B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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