xy and yx are a pair of two digit positive integers with reversed digi

Question

xy and yx are a pair of two digit positive integers with reversed digits. For how many such pairs does yx - xy = y^2 - x^2?

A. 2
B. 3
C. 4
D. 5
E. 6

niks18 · Accepted Answer

yx-xy=y^2-x^2

=>10y+x-10x-y=(y-x)(y+x)

=> 9y-9x-(y-x)(y+x)=0

or  (y-x) =0 =>  either  y=x  or  y+x=9

Now it is given that  xy  &  yx  are a pair of two digit integers, hence  y  is not equal to  x  because in that case there will be only a single no and not a pair

so  y+x=9  the pairs possible are

(1,8), (2,7), (3,6), (4,5) =  4 .........

Option  C

chetan2u · Answer

Hi..

= yx-xy=y^2-x^2...........10y+x-10x-y+(x-y)(x+y)=0.......9(x-y)+(x-y)(x+y)=0..
(y-x)(9-(x+y)=0 
Either x=y or x+y=9.... But pair means x and y should be different otherwise pair would consist of just one number example 22
So numbers with sum of digits as 9 are 
18 and 81
27 and 72
36 and 63
45 and 54

Since pair of numbers is asked 18 and 81 will be same as 81 and 18.

C

SSWTtoKellogg · Answer

Isn't this question's answer supposed to be 5? (9,0), (8,1), (7,2), (6,3), (5,4).

Bunuel · Answer

(9,0) is not possible because 90 reversed is 9, which is not a two-digit integer.

OneLazyBum · Answer

(C)
Lets say, x=a and y=b
Therefore, xy=10a+b and yx =10b+a

So given eqn will be: 
(10b+a)-(10a-b) = b^2-a^2
giving us 
a+b = 9
So pairs will be(1,8)(2,7)(3,6) and (4,5)

xy and yx are a pair of two digit positive integers with reversed digi

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

xy and yx are a pair of two digit positive integers with reversed digi

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia