Two digit number

[geekybiz1]

What is the 2 digit number?

 

1. The number is 3 times sum of its digit.

2. If 45 is added to the number, we get the original number with reversed digits.

[iisan]

i) Let the number be 10a+b

10a+b = 3(a+b)

a = 2b/7

Since a and b are both

(SUFF)

 

ii) (10a+b) + 45 = 10b+a

Adding the units digits of the left and comparing to that of the right,

b+5 = a or b+5 = 10+a

ie., b + 5 = a or a + 5 = b ---- (1)

Adding the tens,

10a+40 = 10b or 10a+40+10 = 10b

ie, a + 4 = b or a + 5 = b ---- (2)

 

From (1) and (2), the only possible relation between a and b is a + 5 = b with b > 5.

Now the possible numbers are 16, 27, 38, 49.

(INSUFF)

 

Ans A

[rits700]

agree with A

[geekybiz1]

Yes, even I got A.

But OA was C, so had a doubt.

It said, since two unknowns, we need two equations. But I didnt agree...

[Linux]

Guys,

 

with a = 2b/7 from statement 1, I believe we have two solutions: a=0, b=0 and a=2, b=7. Can't we?. Therefore the answer is C. Let me know what you think of it.

 

Okay I get it now! when a=0, b=0. then the number is 0, which is not a 2-digit no. Hence A

[crackgmat750]

Hi IISan

 

Can you please eloborate "Adding the units digits of the left and comparing to that of the right" and "Adding Tens"?

 

Thanks

[iisan]

CG750: Solution with additional steps below. Hope this helps.

 

ii) (10a+b) + 45 = 10b+a

Or, 10a + b + 10*4 + 5 = 10b + a

Or, 10(a+4) + (b+5) = 10b + a --- (A)

The sum of the units digits on the left is (b+5).

This should be equal to a, if (b+5)

Or it should be equal to 10+a, if (b+5) >= 10 (with 1 carrying over to the tens digits)

 

Adding the units digits of the left and comparing to that of the right,

b+5 = a or b+5 = 10+a

ie., b + 5 = a or a + 5 = b ---- (1)

Adding the tens,

10a+40 = 10b or 10a+40+10 = 10b

From (A): 10(a+4) + (b+5) = 10b + a

The tens are (a+4) on the left and b on the right

Now, a+4 = b, if the sum of the units digits (b+5)

Or (a+4)+1 = b, if the sum of the units digits >=10 (The "1" on the left is the carry over)

ie, a + 4 = b or a + 5 = b ---- (2)

From (1) and (2), the only possible relation between a and b is a + 5 = b with b > 5.

Now the possible numbers are 16, 27, 38, 49.

(INSUFF)