If a, b, and c represent distinct digits, what is the value of the two

Question

If a, b, and c represent distinct digits, what is the value of the two-digit number ab?

(1) ab*ba = aca

(2) a*b < 10

rohit8865 · Answer

(1) b^2=c

if b =-2 , c= 4
if b= -3 , c=9
a could be 5 or 6
not suff

(2)again same as (1) 
insuff

combining same as above
insuff

Ans E

AnthonyRitz · Answer

I believe that you are misinterpreting the question. a, b, and c represent digits, and ab, ba, and aca represent two two-digit numbers and a three-digit number. These are not products. Like, for instance, if a = 8 and b = 3, then ab would be 83, ba would be 38, etc.

rt9 · Answer

1.suff: 21 12 only combo acceptable as digits are different
2. insuff

answer A

KrishnakumarKA1 · Answer

St 1: Nothing can be predicted. INSUFFICIENT

St 2: (a,b)/(b,a)can be (1,2)(1,3)(1,4).......(1,9), (2,3),(2,4). INSUFFICIENT

St 1 & St 2: for each possible set we will calculate ab*ba, that will be 252, 403, 574, 765,976....

only 12*21 = 252

hence ab can be 12 or 21. INSUFFICIENT

Option E

rt9 · Answer

ab can not be 12, only 21 because aca is 252

vivek2k70 · Answer

11 and 11 is another value

Bunuel · Answer

It is mentioned in the stem that a, b, and c represent  distinct  digits.

RMD007 · Answer

I am sure, you wanted to mention: If a, b, and  C  represent distinct digits

We know a,b,c are different digits.

ab*ba = aca

So from the 2 digit multiplication process, first we will multiply a*b. As we get the unit digit number as a itself, means b = 1.

just plugging the numbers 21 & 12 gives 252, means a=2, b=1, c=5.

Also there is no other integer which gives mutiplication X1 * 1X = X_X
A- sufficient.

Bunuel · Answer

Sure. Edited. Thank you for noticing. +1.

mohshu · Answer

ByjusGMATapp  plz elaborate the stat1 ,, according to me stat 1 is suff and 12,21 is the only combo tat fits in.. thanks

hellosanthosh2k2 · Answer

Statement 1:
  ab  *  ba  =  aca 
=>  (10a+b)(10b+a)  =  100a + 10c + a 
=>  100ab + 10a^2 + 10b^2 + ab  =  100a + 10c + a 
=>  100ab + (a^2 + b^2)10 + ab  =  100a + 10c + a

now comparing units digit on both the sides
  ab = a =>  a= 0  OR  b = 1  => but a cannot be 0, if it were, then aca would be 2-digit number => b = 1

now comparing tens digit on both the sides
  a^2 + b^2 = c 
  a^2 = c - b^2 
  a^2 = c - 1 
  a  =  \sqrt{c - 1} 
 only for c = 1, 2, 5,  \sqrt{c - 1}  yields integer
 if c = 1, a = 0 (which is not possible)
 if c = 2, a = 1 (but b is already 1) => not possible
 so only c = 5, a = 2, possible
so number ab = 21 => sufficient

Statement 2: a * b < 10
 lot of combinations ab = {14, 21, 24} not sufficient

(A)

Anurag06 · Answer

Hi Bunuel

I believe for this, one has to remember or recognise multipliers of 21. Isn't there any simpler or easier method than that?

Please suggest. Thanks!

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If a, b, and c represent distinct digits, what is the value of the two

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