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

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MathRevolution
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N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   13 Dec 2019, 01:15
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E

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25% (medium)

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81% (02:17) correct 19% (02:36) wrong based on 151 sessions
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[GMAT math practice 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. \(746\)
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E
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ajaymahadev
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   26 Jan 2020, 21:57
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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
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   13 Dec 2019, 02:13
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MathRevolution wrote:
[GMAT math practice 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. \(746\)


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
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N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   13 Dec 2019, 03:27
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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

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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   15 Dec 2019, 18:27
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=>

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
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   19 Dec 2019, 09:09
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Plugging the answer values seem to be way faster, just reverse the units and 100 th digits and subtract. Will take around 30 secs
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   26 Jan 2020, 18:31
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MathRevolution wrote:
[GMAT math practice 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. \(746\)


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 :)
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink] New post   20 Nov 2023, 05:06
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Re: N is a 3-digit positive integer. The sum of all 3 digits of N is 17, [#permalink]
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