Pls explain- Digits Problem

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Sat Jul 13, 2013 7:23 pm

A given number C is between 10 and 99 and has the property that if its digits are reversed, the difference between C reverse and C = 36. Furthermore, 3 times the second digit minus 2 times the first digit = 15. What is C's second digit?

I am not clear as to what is said in the second step:

3 times the second digit minus 2 times the first digit =15

Suppose the number is 10a+b

Now the second digit is B(units digit) therefore its equal to =3b and first digit is 10a therefore its equal to 10a*3=30a

Shouldn't the equation be 30a-2b=15

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Source: Beat The GMAT — Problem Solving | Sat Jul 13, 2013 7:23 pm

transporter76: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun May 19, 2013 12:12 amFollowed by: 1 member

by transporter76 » Sat Jul 13, 2013 9:19 pm

Let C=10a+b, 1<=a<=9, 0<=b<=9
reverse of C = 10b+a

(10b+a)-(10a+b) = 36

9b-9a=36
b-a=4 --(1)

3b-2a=15 --(2)

solve (1) and (2)

a=3, b=7

C=37

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Imsukhi: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Thu Jun 20, 2013 7:58 pm; Thanked: 1 times

by Imsukhi » Sat Jul 13, 2013 9:50 pm

Let C=10a+b, 1<=a<=9, 0<=b<=9
reverse of C = 10b+a

(10b+a)-(10a+b) = 36

9b-9a=36
b-a=4 --(1)

3b-2a=15 --(2)

solve (1) and (2)

a=3, b=8

C=38

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 14, 2013 3:22 am

A given number C is between 10 and 99 and has the property that if its digits are reversed, the difference between C reversed and C = 36. Furthermore, 3 times the second digit minus 2 times the first digit = 15. What is C's second digit?

A) 2
B)3
C)4
D)6
E)7

Let T = the tens digit and U = the units digit.

C = 10T + U.
C reversed = 10U + T.

The difference between C reversed and C is 36:
10U + T - (10T + U) = 36
9U - 9T = 36
9(U-T) = 36
U-T = 4.
U-4 = T.

3 times the second digit minus 2 times the first digit is 15:
3U - 2T = 15.

Substituting T=U-4 into 3U - 2T = 15, we get:
3U - 2(U-4) = 15
U + 8 = 15
U = 7.

The correct answer is E.

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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 » Sun Jul 14, 2013 5:49 am

[email protected] wrote:
Shouldn't the equation be 30a-2b=15 ?

Good question.
There's an important difference between the two pieces of given information. One piece (the 2nd piece) provides information about the two individual digits that comprise C, and the other piece (the 1st piece) tells us about the value of the numbers that are created by the individual digits.

If its digits are reversed, the difference between C reversed and C = 36
This tells us about the VALUE of C and the VALUE of reversed C.
To find the value of a number created by a set of digits, we need to consider the place value of each digit.
For example, 157 = (1)(100) + (3)(10) + 7
Likewise, 4298 = (4)(1000) + (2)(100) + (9)(10) + 8

So, if we let a = the tens digit and b = the units digit, then the VALUE of C = 10a + b
The VALUE of C reversed = 10b - a
[see other solutions for what to do from here]

3 times the second digit minus 2 times the first digit = 15
This is somewhat ambiguous, so let's change it to . . .
3 times the units digit minus 2 times the tens digit = 15
Here, we are given information about the two individual digits.
There's no information about the value of C. So, we don't need to multiply the tens digit by 10 (as you did in your solution)
Instead, we can write 3b - 2a = 15

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Jul 14, 2013 6:49 am

GMATGuruNY wrote:
A given number C is between 10 and 99 and has the property that if its digits are reversed, the difference between C reversed and C = 36. Furthermore, 3 times the second digit minus 2 times the first digit = 15. What is C's second digit?

A) 2
B)3
C)4
D)6
E)7
Let T = the tens digit and U = the units digit.

C = 10T + U.
C reversed = 10U + T.

The difference between C reversed and C is 36:
10U + T - (10T + U) = 36
9U - 9T = 36
9(U-T) = 36
U-T = 4.
U-4 = T.

3 times the second digit minus 2 times the first digit is 15:
3U - 2T = 15.

Substituting T=U-4 into 3U - 2T = 15, we get:
3U - 2(U-4) = 15
U + 8 = 15
U = 7.

The correct answer is E.

How do you know that the second digit and first digits refers to the Units or tens digits? Or even vice versa ?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jul 14, 2013 3:35 pm

faraz_jeddah wrote:
GMATGuruNY wrote:
A given number C is between 10 and 99 and has the property that if its digits are reversed, the difference between C reversed and C = 36. Furthermore, 3 times the second digit minus 2 times the first digit = 15. What is C's second digit?

A) 2
B)3
C)4
D)6
E)7
Let T = the tens digit and U = the units digit.

C = 10T + U.
C reversed = 10U + T.

The difference between C reversed and C is 36:
10U + T - (10T + U) = 36
9U - 9T = 36
9(U-T) = 36
U-T = 4.
U-4 = T.

3 times the second digit minus 2 times the first digit is 15:
3U - 2T = 15.

Substituting T=U-4 into 3U - 2T = 15, we get:
3U - 2(U-4) = 15
U + 8 = 15
U = 7.

The correct answer is E.
How do you know that the second digit and first digits refers to the Units or tens digits? Or even vice versa?

Because we read left to right, I interpreted that first digit = tens digit and that second digit = units digit.
The GMAT would not require us to make this sort of interpretation.
On the GMAT, the last sentence would likely read as follows:
The difference between 3 times the units digit of C and 2 times the tens digit of C is 15.

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Jul 14, 2013 3:36 pm

Gracias!

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