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What is the largest possible value of N

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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Feb 03, 2017 5:02 am
RajeshP wrote:Need help.

N is a two-digit number. The sum of its digits is S and the product of its digits is P. What is the largest possible value of N?

(1) N+S=103
(2) 2N=2S+9P
No matter what the statements say, the largest possible value of N can ALWAYS be determined.
For each statement, we can simply test two-digit integers -- starting with 99 and working our way down -- until we find the largest that satisfies the given constraints.
Thus, each statement must be SUFFICIENT.

The correct answer is D
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by jack0997 » Mon Feb 13, 2017 9:09 pm
RajeshP wrote:Need help.

N is a two-digit number. The sum of its digits is S and the product of its digits is P. What is the largest possible value of N?

(1) N+S=103
(2) 2N=2S+9P

OA: D
Hello experts,

I did not get this one. Pl. help. I did this way...

Let the number be N=10x+y; x->tens digit and y-> unit

S=x+y and P=xy

From I stat...

N + S = 103

So, 10x + y + x + y = 103

11x+2y =103

Now how to proceed?

Same with II stat..

2N = 2S + 9P

2(10x + y) = 12(x + y) + 9xy
20x + 2y = 2x + 2y + 9xy
18x = 9xy
y = 2

How to find x? Pl. help.
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by Jay@ManhattanReview » Mon Feb 13, 2017 9:27 pm
jack0997 wrote:
RajeshP wrote:Need help.

N is a two-digit number. The sum of its digits is S and the product of its digits is P. What is the largest possible value of N?

(1) N+S=103
(2) 2N=2S+9P

OA: D
Hello experts,

I did not get this one. Pl. help. I did this way...

Let the number be N=10x+y; x->tens digit and y-> unit

S=x+y and P=xy

From I stat...

N + S = 103

So, 10x + y + x + y = 103

11x+2y =103

Now how to proceed?

Same with II stat..

2N = 2S + 9P

2(10x + y) = 12(x + y) + 9xy
20x + 2y = 2x + 2y + 9xy
18x = 9xy
y = 2

How to find x? Pl. help.
Hi jack0997,

You did all fine. Let's pick up from where you left.

S1: N+S=103

.
.
.
.
You reached here: 11x+2y =103.

This is a linear equation with two variable; though you cannot get a unique solution, you can get consistent solutions.

Since the question asks for the largest possible value of the two digit number N, the tens digit would be 9.

Let's plug in x=9 in 11x+2y =103.

=> 11*9+2y =103.

=> y = (103-99)/2 = 2

=> Largest possible value of N =92. Sufficient.

Let us take statement 2.

S2: 2N=2S+9P
.
.
.
You reached here: y = 2

Your challenge is that since x vanishes how to get the value of x?

Remember that in this situation the equality is true for any value of x: 1, 2, 3, ...., 9.

Among these the largest is 9, so we pick x=9.

So, the largest possible number =92. Sufficient.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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