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What is the two-digit number N? [#permalink]
 03 Nov 2012, 08:48
Question Stats:
72% (01:57) correct
28% (01:05) wrong based on 0 sessions
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.
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Re: What is the two-digit number N? [#permalink]
03 Nov 2012, 10:07
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.
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Re: What is the two-digit number N? [#permalink]
03 Nov 2012, 17:43
monikaleoster wrote: 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. 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.
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Re: What is the two-digit number N? [#permalink]
04 Nov 2012, 12:32
Bunuel wrote: 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. Even when we combine both the statements, N can be 54 or 45, right? So isn't the answer E?
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Re: What is the two-digit number N? [#permalink]
04 Nov 2012, 14:50
Argon wrote: Bunuel wrote: 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. Even when we combine both the statements, N can be 54 or 45, right? So isn't the answer E? N cannot be 45, because 45-54=-9 not 9 as stated in (1).
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
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Re: What is the two-digit number N?
[#permalink]
04 Nov 2012, 14:50
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