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Difficulty:
35%
(medium)
Question Stats:
66% (01:44) correct
34%
(01:38)
wrong
based on 146
sessions
History
Date
Time
Result
Not Attempted Yet
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
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
gmatcafe
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.
_________________
General Discussion
rocky620
Retired Moderator
Joined: 10 Nov 2018
Last visit: 11 May 2023
Posts: 476
Location: India
Concentration: General Management, Strategy
Schools: IIMA PGPX'22 IIMB EPGP'22 IIMC PGPEX'22 ISB'22
GMAT 1: 590 Q49 V22
WE:Other (Retail: E-commerce)
The answer should be 10
23,32, 34,43, 45,54, 67,76, 89,98
23,32, 34,43, 45,54, 67,76, 89,98
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
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
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
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
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.
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.
Posts: 4
Can anyone tell me why the answer is not 9?
10
21
32
43
54
65
76
87
98
10
21
32
43
54
65
76
87
98
gagankhanna08
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
gagankhanna08
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 ....
gagankhanna08
@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.
rocky620
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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