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How many integers n greater than 10 and less than 100 a

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Concentration: General Management, Technology
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How many integers n greater than 10 and less than 100 a  [#permalink]

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New post 23 Nov 2018, 07:41
1
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Difficulty:

  55% (hard)

Question Stats:

53% (01:56) correct 48% (03:13) wrong based on 39 sessions

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How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

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Re: How many integers n greater than 10 and less than 100 a  [#permalink]

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New post 23 Nov 2018, 07:55
1
HKD1710 wrote:
How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

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Let n=ab(as it is 2 digit number bcz >10 and less than 100)
so reverse will be =ba

now as per qsn
reverse-orgn=9--------(1)

we know ab can be written as 10*a+b(54=10*5+4)
ba=10*b+a

now substituting in 1

10b+a-10a-b=9
9b-9a=9
b-a=1
so this condition will hold true only if diff of two digits is 1

so from 11 to 20
this is true only for 12(2-1=1)

then from 21-30 true for 23(3-2=1) make sure 21 is not valid as(1-2=-1 not 1) b-a=1
so this way
each set of 10 numbers has 1 number for which b-a=1
total we have 9 such sets (11-20,21-30,---91-99)
so 8 such numbers bcz in 91-99 we cant have this condition

i.e 12,23,34,45,56,67,78,89,
so 8 such numbers
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How many integers n greater than 10 and less than 100 a  [#permalink]

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New post 23 Nov 2018, 10:51
1
Let A be tens digit & B be units digit

\(X = 10A + B\)

After reversing digits, \(X _{new}\) \(= 10B + A\)

Difference between \(X\) and \(X_{new}\) is \(9\), so I get following equation

\((10A + B) - (10B + A) = 9\)

\(9A – 9B = 9\)

\(9(A-B) = 9\)

\(A-B = 1\)

\(A = B+1\)

Since units digit X is +1 more than tens digit, I get following numbers

12, 23, 34, 45, 56, 67, 78, 89

IMO: D :)
GMAT Club Bot
How many integers n greater than 10 and less than 100 a &nbs [#permalink] 23 Nov 2018, 10:51
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How many integers n greater than 10 and less than 100 a

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