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# N is a 3-digit number, and the sum o

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CEO
Joined: 11 Sep 2015
Posts: 3446
N is a 3-digit number, and the sum o  [#permalink]

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11 Jun 2018, 06:01
Top Contributor
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:19) correct 48% (02:17) wrong based on 62 sessions

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N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions

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Re: N is a 3-digit number, and the sum o  [#permalink]

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11 Jun 2018, 06:34
1

Solution

Given:
• N is a 3-digit number
• Sum of the digits of N is 10
• When N is reversed, the new number is 99 less than N

To find:
• The value of N

Approach and Working:
If we assume N = abc, then reverse of N = cba

As N – reverse of N = 99, we can write,
• abc – cba = 99
Or, 100a + 10b + c – 100c – 10b – a = 99
Or, 99 (a – c) = 99
Or, a – c = 1

As both a and c are single-digit integers, the possible values of (a, c) = (2, 1), (3, 2), (4, 3), (5, 4)
[(6, 5) onwards values are not possible as sum of the digits is equal to 10]

Using the relation, a + b + c = 10, the possible value sets of (a, b, c) = (2, 7, 1), (3, 5, 2), (4, 3, 3), (5, 1, 4)

Analysing Statement 1
• As per the information given in statement 1, a = 1 + c
o This is an information that we have already derived, and not giving us any new information

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in statement 2, b = 2 + a
• From the possible values of (a, b, c) we can have only one case where it is getting satisfied = (3, 5, 2)
Therefore, the number N = 352

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

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Re: N is a 3-digit number, and the sum o  [#permalink]

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11 Jun 2018, 06:35
1
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions
Let's represent N as abc where:

a = hundreds digit
b = tens digit
c = ones digit

Therefore algebraically:

N = 100a + 10b + c

Reverse N = 100c + 10b + a

Given: N = Reverse N + 99
----> 100a + 10b + c = 100c + 10b + a + 99

Simplify: 99a = 99c + 99 -----> a = c + 1

From given info we know:
a = c + 1
a + b + c = 10

Our goal is to solve for N by finding a,b and c

Statement 1
Tells us a = c + 1. We already know this info so its not helpful
-------> INSUFFICIENT

Statement 2 says b = a + 2

Therefore everything can be written in terms of a:
a = a
b = a + 2
c = a - 1

Since a + b + c = 10
----> a + (a+2) + (a - 1) = 10

----> a = 3
----> c = 2
----> b = 5

Therefore N is 352.
-------------------------> sufficient

Sent from my SM-G920T using GMAT Club Forum mobile app
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N is a 3-digit number, and the sum o  [#permalink]

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11 Jun 2018, 08:25
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions

Since we get a 3-digit number(reversed) after subtracting 99 from N(3-digit integer), therefore N must be greater than 200.

Property:- When the digits of a 3-digit number are reversed after subtracting the original number by 99, the hundred's place digit is one more than the unit's place digit.

Question stem:- N=?

Statement1:- As mentioned above in the property, this statement doesn't provide additional info. So, st1 is insufficient.

Statement-2

The affixed table may be referred.

From the table, N=352.

Hence, statement2 is sufficient.

Ans. B

Hope my logic is correct.
Attachments

File comment: I stopped checking at 100th digit=3 because any positive integer thereafter yields sum of digits>10.

N-3 digit.JPG [ 27.35 KiB | Viewed 467 times ]

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PKN

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N is a 3-digit number, and the sum o  [#permalink]

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11 Jun 2018, 13:24
1
1
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions

We are given the following information in the question stem:
1. Let N(3 digit number) be xyz where x - hundred's digit, y - ten's digit, z - one's digit.
2. x+y+z = 10.
3. xyz - zyx = 99(Here zyx is the reverse of the number N)

We have been asked the value of N.

1. When the hundred's digit of N is 1 more than it's units digit, there are 4 possibilities: 271,352,433,514.
Reversing these 4 numbers we will get 172,253,334,415 & each of these 4 numbers when subtracted from
the number it reverses, gives us 99. We can't find a unique value for N. (Insufficient)

2. If the tens digit of N is 2 more than its hundreds digit, there are 3 possibilities: 136,244,352. Reversing
these 3 numbers, we will get 631,442,253. Only 352 - 253 gives 99, making 352 our number (Sufficient - Option B)
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Re: N is a 3-digit number, and the sum o  [#permalink]

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13 Jun 2018, 07:29
Top Contributor
GMATPrepNow wrote:
N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N. What is the value of N?

(1) The hundreds digit of N is 1 more than its units digit.
(2) The tens digit of N is 2 more than its hundreds digit.

*kudos for all correct solutions

Target question: What is the value of N?

Given: N is a 3-digit number, and the sum of its digits is 10. When the digits of N are reversed, the new number is 99 less than N.
Let N = wxy, where w, x and y represent the 3 digits in N
So, the first equation we can write is: w + x + y = 10

Now let's examine the situation where we REVERSE the digits.
First of all, the VALUE of N (wxy) is equal to 100w + 10x + y
Next, the VALUE of the REVERSED number (yxw) is equal to 100y + 10x + w
Since the REVERSED number is 99 less than N, we can write: 100y + 10x + w = 100w + 10x + y - 99
Subtract w from both sides: 100y + 10x = 99w + 10x + y - 99
Subtract 10x from both sides: 100y = 99w + y - 99
Subtract y from both sides: 99y = 99w - 99
Divide both sides by 99 to get: y = w - 1

Now onto the statements....

Statement 1: The hundreds digit of N is 1 more than its units digit.
In other words, w = y + 1, which is the SAME as y = w - 1
Notice that this provides NO NEW INFORMATION, since we already concluded that y = w - 1
Since statement 1 provides no new information, it is NOT SUFFICIENT

Statement 2: The tens digit of N is 2 more than its hundreds digit.
In other words, x = w + 2
Now that we've written x and w in terms of w (i.e., x = w + 2 and y = w - 1), we can take the given information (w + x + y = 10), and replace w and x
When we do so, we get: w + (w + 2) + (w - 1) = 10
Simplify: 3w + 1 = 10
Solve: w = 3
If w = 3, then x = 5, and y = 2
So, N =352
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: N is a 3-digit number, and the sum o   [#permalink] 13 Jun 2018, 07:29
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