Hi all ,
I have a question from the online gmat all the quant companion -
Chapter 1 has a question on page 6 :
AB
CA
DEBC
In the multiplication above, each letter stands for a different non-zero digit, with
A × B < 10. What is the two-digit number AB?
(A) 23 (B) 24 (C) 25 (D) 32 (E) 42
My question is , do I have to do long multiplication till tens digit to solve or is there a better strategy?
Many thanks !
GMAT Forum
2 postsPage 1 of 1
- KarishmaD187
- Course Students
- Posts: 2
- Joined: Mon Mar 20, 2017 6:43 am
- TiffanyB
- ManhattanGMAT Staff
- Posts: 41
- Joined: Mon Dec 30, 2019 4:13 pm
Re: Question on approach for unknown digits problem
Hello KarismaD187,
I'm not exactly sure how you went about solving based on your question. Based on your statement (above), I believe that you did what I'm about to describe. If I'm understanding your question and process correctly, then yes you do need to multiply up to tens digits.
In regards to the "best way" to solve, one of the best aspects of the GMAT is that there are often MANY ways to solve a problem!
The solution method that I prefer for this problem is to work backwards. I recognized this by first looking at the information in the problem and realizing that I could choose numbers 1-9 for each letter, but that this would be time consuming.
Next, I looked at the answer choices and realized that they represented potential values of AB. This is my clearest path forward, especially as A appears in the second number, CA, and B appears in the product, DEBC.
Thinking more critically, one other important piece of information is that I recognize that my product will require two rows, which are added together. However, in the second row, the units place is always 0 so C = A x B.
I started with A and got the following:
23
_2
??46
???0
Now I know that C = 6 in this case, so I can get more detailed:
23
62
??46
??80
??26
The B values (bolded) are not equal. Eliminate A.
I tried B and got the following:
24
?2
??48
Now I know that C = 8, so:
24
82
??48
??20
??68
The Bs are not equal. Eliminate B.
Here is answer choice C:
25
?2
??50
This one has two big issues that I spot immediately. The problem states that each number is a non-zero digit. Also, the problem states that A x B < 10, but in this answer choice A x B = 10. This one is incorrect.
Answer choice D:
C = 6
32
63
??96
??20
??16
Bs aren't equal. Eliminate D.
Answer choice E:
This has to be correct, because everything else has been eliminated.
C = 4*2 = 8
42
84
??68
??60
??28
And FINALLY the Bs match. This one is correct.
KarishmaD187 Wrote:My question is , do I have to do long multiplication till tens digit to solve or is there a better strategy?
Many thanks !
I'm not exactly sure how you went about solving based on your question. Based on your statement (above), I believe that you did what I'm about to describe. If I'm understanding your question and process correctly, then yes you do need to multiply up to tens digits.
KarishmaD187 Wrote:Hi all ,
I have a question from the online gmat all the quant companion -
Chapter 1 has a question on page 6 :
AB
CA
DEBC
In the multiplication above, each letter stands for a different non-zero digit, with
A × B < 10. What is the two-digit number AB?
(A) 23 (B) 24 (C) 25 (D) 32 (E) 42
In regards to the "best way" to solve, one of the best aspects of the GMAT is that there are often MANY ways to solve a problem!
The solution method that I prefer for this problem is to work backwards. I recognized this by first looking at the information in the problem and realizing that I could choose numbers 1-9 for each letter, but that this would be time consuming.
Next, I looked at the answer choices and realized that they represented potential values of AB. This is my clearest path forward, especially as A appears in the second number, CA, and B appears in the product, DEBC.
Thinking more critically, one other important piece of information is that I recognize that my product will require two rows, which are added together. However, in the second row, the units place is always 0 so C = A x B.
I started with A and got the following:
23
_2
??46
???0
Now I know that C = 6 in this case, so I can get more detailed:
23
62
??46
??80
??26
The B values (bolded) are not equal. Eliminate A.
I tried B and got the following:
24
?2
??48
Now I know that C = 8, so:
24
82
??48
??20
??68
The Bs are not equal. Eliminate B.
Here is answer choice C:
25
?2
??50
This one has two big issues that I spot immediately. The problem states that each number is a non-zero digit. Also, the problem states that A x B < 10, but in this answer choice A x B = 10. This one is incorrect.
Answer choice D:
C = 6
32
63
??96
??20
??16
Bs aren't equal. Eliminate D.
Answer choice E:
This has to be correct, because everything else has been eliminated.
C = 4*2 = 8
42
84
??68
??60
??28
And FINALLY the Bs match. This one is correct.
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