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

Question

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

chetan2u · Accepted Answer

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.

rocky620 · Answer

The answer should be 10

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

AbhinavSV · Answer

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

AnirudhaS · Answer

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

JeremySkidmore29 · Answer

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.

gagankhanna08 · Answer

Can anyone tell me why the answer is not 9?

10
21
32
43
54
65
76
87
98

JeremySkidmore29 · Answer

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

AnirudhaS · Answer

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 ....

AbhinavSV · Answer

@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.

Nikkony · Answer

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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