Data Sufficiency

A number B is formed by reversing the two digit number A. What are the digits of A?
(1) Difference of A and B lies between 70 and 80
(2) B is a two digit number

I don't have the OA. Detailed explanations would be appreciated

this is a hard prob and I aint a wizard at quant- i'll give it a try :

a=10x + y
b=10y + x

find x,y

stat 1 :

70< 9x-9y <80

less than 8 < x-y < less than 9. {dividing throughout by 9}


since x - y = positive integer therefore x-y = 8

thus,x should be 91 and Y = 19 - sufficient


stat :2
y not equal to 0 - I dont think this is of any use.

answer - A.


I might be hopelessly wrong - but I posted to stand corrected.

Hi,
I think bblast got it almost correct.
From(1):
x-y = 8
So, (x,y) can be (9,1) or (8,0)
Not sufficient

From(2):
Not sufficient

Both(1) and (2):
B is two digit number
So, y can't be 0.
So, (x,y) = (9,1)

Hence, C

Can you post the source of this.

Thanks frank- getting q's almost correct wont help me . But ya this was a bit hard.

I would also like to know the source of this good question.

since the difference is between 70 and 80 you know that A must be greater than 70, and that the units digit is probably 0 or 1 (any higher and you are subtracting somethign in the 20's which would result in something less than 70). Try 80 - 08= 72 so that works but so does 91 - 19 = 72. You have two different answers that work so BCE

if B is a two digit number this means that A does not end in 0 - but that doesn't help by itself - CE

But if the two choices from A are 80 and 91 and A can't end in a 0 that means that A must be 91 and the answer is C.

Great question with a lot of strategic value - thanks for sharing!

If you didn't think through the lens of algebra you can still attack this one using just arithmetic. You need a difference of at least 70 so you have to start with a number that's 70+ and subtract something that's less than 20. That limits your options...especially if you're thinking of 2-digit numbers forward and backward because then you're subtracting something in the teens.

81 - 18 = 63...not enough
91 - 19 = 72...this one works!
92 - 29 = already too small

So you'd think at first that 91 and 19 is your only combination.

Here's where Data Sufficiency strategy comes in. Statement 2 alone looks pretty useless. I sort of already assumed that B was two digits, so why are they telling me that? If you read those pretty bland/useless statements by thinking "Why Are You Here?", they often tell you something really important - in this case, it's telling me that I don't have to use a number B that's in the teens...I could use a single digit number like 08 or 09. Well, that allows for 80-08 = 72 - another possibility that shows me that statement 2 alone is not sufficient. I need both to finally arrive at 91-19. So the answer is C, and I learned that by trying to determine why statement 2 even existed.

Here, the role of statement 2 is to make explicit a rule that most of us probably assumed in the first place. In events like that, you need to ask yourself whether that rule needed to be made explicit or not. And going back to the question, the only thing we know is that we reversed 2-digit number A...we don't know at all that B remains at two digits until statement 2 explicitly defines that.

Brian@VeritasPrep wrote:Great question with a lot of strategic value - thanks for sharing!

Here's where Data Sufficiency strategy comes in. Statement 2 alone looks pretty useless. I sort of already assumed that B was two digits, so why are they telling me that? If you read those pretty bland/useless statements by thinking "Why Are You Here?", they often tell you something really important - in this case, it's telling me that I don't have to use a number B that's in the teens...I could use a single digit number like 08 or 09. Well, that allows for 80-08 = 72 - another possibility that shows me that statement 2 alone is not sufficient. I need both to finally arrive at 91-19. So the answer is C, and I learned that by trying to determine why statement 2 even existed.

Aren't we reading the question incorrectly here
1) statement ambiguous... says difference of i.e., 70 < |A-B| < 80
if this is correct then from 1) & 2) A could be 19 or 91.

Further more the question asks what are the digits of A?
in general someone will answer 1 & 9 or one may say 9 & 1. (place value not given importance here )

so answer is C. I don't think A=91

correct me if I am wrong...

i used this general method to solve, much easier than trying numbers i think
x and y = digits
so
A = 10X + Y
B = 10Y + X

1) 70 < difference < 80
|A-B| = 9|X-Y|
therefore, 70 < 9|X-Y| < 80
gives X-Y = 8
possible values 9,1 or 8,0
both satisfy so INSUFFICIENT

2) B is 2 digit number
INSUFFICIENT

1) & 2) together
8,0 = get out mate
only remains 1,9
so answer C