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Can we backsolve this question basis answer choices please?

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by Brent@GMATPrepNow » Sat Mar 29, 2014 7:16 am
[email protected] wrote:Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?

A. 153
B. 150
C. 137
D. 129
E. 89
IMPORTANT: If we're going to halve each digit to get two new digits, the two original digits MUST BE EVEN.

So, the LARGEST possible 2-digit number (with EVEN digits) is 88
If we halve each digit, we get 44
88 + 44 = 132
So, the largest possible SUM is 132.
This means we can ELIMINATE A, B and C

Now let's check the remaining answer choices.
Answer choice D (129), is very close to the largest possible sum (132) that we just calculated. So, let's fiddle with those numbers to see whether we can get a sum of 129

How about 86? (the 2nd largest value for the original number)
If we halve each digit, we get 43
86 + 43 = 129 . . . we have a MATCH

So, the correct answer must be D

Cheers,
Brent
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by [email protected] » Sat Mar 29, 2014 7:21 am
great approach Brent, thanks!

Brent@GMATPrepNow wrote:
[email protected] wrote:Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H?

A. 153
B. 150
C. 137
D. 129
E. 89
IMPORTANT: If we're going to halve each digit to get two new digits, the two original digits MUST BE EVEN.

So, the LARGEST possible 2-digit number (with EVEN digits) is 88
If we halve each digit, we get 44
88 + 44 = 132
So, the largest possible SUM is 132.
This means we can ELIMINATE A, B and C

Now let's check the remaining answer choices.
Answer choice D (129), is very close to the largest possible sum (132) that we just calculated. So, let's fiddle with those numbers to see whether we can get a sum of 129

How about 86? (the 2nd largest value for the original number)
If we halve each digit, we get 43
86 + 43 = 129 . . . we have a MATCH

So, the correct answer must be D

Cheers,
Brent
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by [email protected] » Sat Mar 29, 2014 6:27 pm
Hi shibsriz,

Brent has pointed out one of the key elements to this question: the digits MUST be EVEN.

You can TEST THE ANSWERS on this question. Here's how....

The question mentions that G is "halved" to form H. In algebra terms, this means...

H = G/2

When the question asks for what COULD be the sum of G and H, what it's REALLY asking is...

Which of these could be the value 1.5G (given the constraints of the question)?

Let's TEST answer E...

1.5G = 89

Now multiply both sides by 2 to get rid of the decimal...

3G = 178

178 is NOT evenly divisible by 3, so it CAN'T be the answer.

Let's TEST answer D...

1.5G = 129
3G = 258

G = 86; this IS a 2-digit number with EVEN digits!!!!

G=86, H=43, G+H = 129
This matches everything we were told in the prompt.

Final Answer: D

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