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monikaleoster
03 Nov 2012, 08:48
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C
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Difficulty:
35%
(medium)
Question Stats:
67% (01:44) correct
33%
(01:39)
wrong
based on 564
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What is the two-digit number N?
(1) The difference between N and the number formed by reversing its digits is 9.
(2) The number N is divisible by 9.
(1) The difference between N and the number formed by reversing its digits is 9.
(2) The number N is divisible by 9.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Nov 2012, 10:07
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What is the two-digit number N?
Any two-digit integer can be represented as 10a+b (wher a and b are singel digit integers), for example 37=3*10+7, 88=8*10+8, etc.So, let's say N=10a+b.
(1) The difference between N and the number formed by reversing its digits is 9 --> (10a+b)-(10b+a)=9 --> a-b=1 --> N can be: 21, 32, ... Not sufficient.
(2) The number N is divisible by 9 --> in order a number to b divisible by 9, the sum of its digit must b divisible by 9. Thus we are given that a+b=9 (in this case N can be 18, 27, 36, 45, 54, 63, 72, 81, or 90) or a+b=18 (in this case N can only be 99). Notice that a+b cannot be a multiple of 9 more than 18, since a and b are single digit integers. Not sufficient.
(1)+(2) N cannot be 99 (a+b=18), since 99-99=0 not 9 as (1) states. So, we have that a-b=1 and a+b=9 --> a=5 and b=4, thus N=54. Sufficient.
Answer: C.
Hope it's clear.
Any two-digit integer can be represented as 10a+b (wher a and b are singel digit integers), for example 37=3*10+7, 88=8*10+8, etc.So, let's say N=10a+b.
(1) The difference between N and the number formed by reversing its digits is 9 --> (10a+b)-(10b+a)=9 --> a-b=1 --> N can be: 21, 32, ... Not sufficient.
(2) The number N is divisible by 9 --> in order a number to b divisible by 9, the sum of its digit must b divisible by 9. Thus we are given that a+b=9 (in this case N can be 18, 27, 36, 45, 54, 63, 72, 81, or 90) or a+b=18 (in this case N can only be 99). Notice that a+b cannot be a multiple of 9 more than 18, since a and b are single digit integers. Not sufficient.
(1)+(2) N cannot be 99 (a+b=18), since 99-99=0 not 9 as (1) states. So, we have that a-b=1 and a+b=9 --> a=5 and b=4, thus N=54. Sufficient.
Answer: C.
Hope it's clear.
Archit143
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03 Nov 2012, 17:43
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monikaleoster
Let the num N = 10x + Y
wher x and y are the unit and tens places
from statement 1 we get
10x + y - 10y - x =9
ie 9x - 9y = 9
x - y = 1
Not sufficient
Statement 2
n = 9p
not sufficient
Combining we get
N = 9p >>>>>>>>>> 9, 18, 27,36,45,54
as per statement 1 Tenth digit - unit digit = 1
i.e 54 = 5-4 =1
C is the answer.
