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11 Jun 2018, 07:01
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B
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Difficulty:
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56% (02:28) correct
44%
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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.
(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.
11 Jun 2018, 07:34
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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)
Hence, statement 2 is sufficient to answer
Hence, the correct answer is option B.
Answer: B
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Expert reply
11 Jun 2018, 07:35
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GMATPrepNow
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
Answer: B
Sent from my SM-G920T using GMAT Club Forum mobile app
