N is a 3-digit positive integer. The sum of all 3 digits of N is 17,

Question

N  is a  3 -digit positive integer. The sum of all  3  digits of  N  is  17 , and the sum of its hundreds digit and its units digit is  13.  The new number, which is made by exchanging the digits in the hundreds position and the units digit, 00000  is  99  less than the original number  N.  What is the value of  N ?

A.  944 
 
B.  449 
 
C.  548 
 
D.  845 
 
E.  746

ajaymahadev · Accepted Answer

I think that it is better to check the individual options with the given conditions. In 10 seconds, we can find that the first 2 conditions are useless since they are obeyed by all the options. So the only thing that we can work with is the last condition that the difference is 99.

A 944 449 - difference not near 100

B. 449 - 944 difference not near 100

C. 548 - 845 difference not near 100

D. 845 - 548 difference not near 100

E. 746 - 647 difference is 99 so this is our correct answer

rajatchopra1994 · Answer

Explanation:

Let 3 digit number is = xyz
x+y+z=17
x+z=13
y=17-13=4
So the middle number is 4
now, when digit reverses change is 99.
An only possible option is E, 746-647 = 99

IMO-E

ManjariMishra · Answer

Let the number be ABC

A+B+C = 17
A+C=13
CBA = ABC -99
100C + 10B + A = 100A +10 B +C -99
99A-99C -99 =0
A-C =1
Solving the equation we get 
A=7 B=4 C=6

746 E is the answer

Posted from my mobile device

MathRevolution · Answer

=>

Assume  N  is a three-digit integer represented by  xyz.

Then we have an algebraic expression  N = 100x + 10y + z.

We have  x + y + z = 17, x + z = 13  and  100z + 10y + x = 100x + 10y + z – 99.

If we subtract the first  2  equations we get  (x + y + z) – (x + z) = 17 – 13  and  y = 4.

When we substitute this into the last equation, we have  100z + 10*4 + x = 100x +10*4 + z - 99, 99z – 99x = -99.  If we multiply by  -1  we get  99x - 99z = 99  or  x – z = 1.

Then we have  x = 7  and  z = 6,  since  x + z = 13  and  x – z = 1.

So, the original number  N  is  746.

Therefore, E is the answer.
Answer: E

PinakiRDas · Answer

Plugging the answer values seem to be way faster, just reverse the units and 100 th digits and subtract. Will take around 30 secs

TheNightKing · Answer

First thing, can someone confirm what are those 000000? The options give you the reverse so you dont even have to take effort. Clearly between A and B & between C and D the difference is greater than 99. That leaves us with E. 53 seconds

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

N is a 3-digit positive integer. The sum of all 3 digits of N is 17,

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

My Rewards

GMAT Problem Solving (PS) Questions

N is a 3-digit positive integer. The sum of all 3 digits of N is 17,

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

My Rewards