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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