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How many two-digit positive integers are increased by nine when their

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Russ19
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How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 07:51
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How many two-digit positive integers are increased by nine when their digits are reversed?

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10
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C
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chetan2u
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How many two‐digit numbers increase by 9 when their digits are reverse [#permalink] New post   25 Jan 2022, 23:46
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gmatcafe wrote:
How many two‐digit numbers increase by 9 when their digits are reversed?
A. 5
B. 6
C. 7
D. 8
E. 4



Let the initial number be xy or 10x+y.
When the digits are reversed, the number becomes yx or 10y+x

Thus, 10x+y+9=10y+x......y=x+1
So all numbers where tens digit is 1 less than units digit => 12, 23, 34, 45, 56, 67, 78, 89
Total - 8


D

The choices in the GMAT are in order, so E requires to be changed and please search before posting a question.
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 08:20
The answer should be 10

23,32, 34,43, 45,54, 67,76, 89,98
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How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 10:56
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Any 2 digit number with ten's digit x and one's digit y can be written in form 10x+y.
So,
Actual number: 10x+y;
After digit reversal:10y+x

According to given condition
\(10y+x -(10x+y) = 9\)
\(9y-9x=9\)
\(y-x=1\)
\(y=x+1;\)

to satisfy this x can only range from 1 to 8 inclusive;

Hence Answer: 8
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AnirudhaS
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 12:04
the numbers are:

12
23
34
45
56
67
78
89

the pattern is easy to spot, the tens digit is 1 less than the unit digit

Answer: C
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JeremySkidmore29
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 12:50
I spotted a pattern and did what Anirudhas did

12 -- 21
23 --- 32
34 --- 43

This pattern can be continued through 8, and it would reverse once you get to 9.

The problem took me a bit too long for how easy the pattern was, took a bit over 2 mins for me to solve.
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 13:58
Can anyone tell me why the answer is not 9?

10
21
32
43
54
65
76
87
98
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JeremySkidmore29
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 14:08
gagankhanna08 wrote:
Can anyone tell me why the answer is not 9?

10
21
32
43
54
65
76
87
98


The number has to increase by 9. So 98 would be 89 which would be a decrease.

Reread the question slowly. This happens to me a lot and is so aggravating lol
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AnirudhaS
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   29 Sep 2020, 14:09
gagankhanna08 wrote:
Can anyone tell me why the answer is not 9?

10
21
32
43
54
65
76
87
98

Please read the question carefully. It says when you increase the said number by 9 its digits are reversed.

10+9=19 now is the digits reversed? NO
21+9=30, are the digits reversed? Again no
The pattern is 12, 23, 34 ....
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   30 Sep 2020, 09:44
gagankhanna08 wrote:
Can anyone tell me why the answer is not 9?

10
21
32
43
54
65
76
87
98


@gagankanna08 .Question says when you reverse the digits, numbers should increase by 9

but the numbers you are listing gets decreased when digits are reversed.
So the correct list would be 12,23,34........
01 wont be in the list as it is not a 2 digit number.
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Nikkony
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Re: How many two-digit positive integers are increased by nine when their [#permalink] New post   04 Oct 2020, 07:43
rocky620 wrote:
The answer should be 10

23,32, 34,43, 45,54, 67,76, 89,98


hi rocky620!

just put it this way:

12 => 21 = 1
23 => 32 = 2
34 => 43 = 3
45 => 54 = 4
56 => 65 = 5
67 => 76 = 6
78 => 87 = 7
89 => 98 = 8

Tot= 8

Hope this helps!
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gmatclubot
Re: How many two-digit positive integers are increased by nine when their [#permalink]
04 Oct 2020, 07:43
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