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How many integers n greater than 10 and less than 100 are such that, i
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04 Jun 2022, 03:30
04 Jun 2022, 03:30
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Question Stats:
83% (01:15) correct
16% (02:02) wrong based on 6 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
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
How many integers n greater than 10 and less than 100 are such that, i
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04 Jun 2022, 04:25
04 Jun 2022, 04:25
1
Ans:(D) 8 .
Explanation:
Let's get this by listing method for clear understanding .
Groups The no. Reversed no
11-20. 12. 21
21-30. 23. 32
31-40. 34. 43
41-50. 45. 54
51-60. 56. 65
61-70. 67. 76
71-80 78. 87
81-90. 89. 98
91-99. None. None.
The no. Of such kinds are 8.
Posted from my mobile device
Explanation:
Let's get this by listing method for clear understanding .
Groups The no. Reversed no
11-20. 12. 21
21-30. 23. 32
31-40. 34. 43
41-50. 45. 54
51-60. 56. 65
61-70. 67. 76
71-80 78. 87
81-90. 89. 98
91-99. None. None.
The no. Of such kinds are 8.
Posted from my mobile device
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Re: How many integers n greater than 10 and less than 100 are such that, i
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04 Jun 2022, 07:51
04 Jun 2022, 07:51
1
Carcass 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
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
If the digits of n are reversed, the resulting integer is n+9 ?
Let's say n = xy (where x is the tens digit of n, and y is the units digit of n).
So, the VALUE of n = 10x + y (in the same way the value of 29 = (2)(10) + 9)
When we REVERSE the digits of n, we get yx, which means the VALUE of yx = 10y + x
The question tells us the resulting number is 9 greater than the original number (n)
So, we can write: 10y + x = 10x + y + 9
Subtract y from both sides: 9y + x = 10x + 9
Subtract 10x from both sides: 9y - 9x = 9
Divide both sides by 9 to get: y - x = 1
This tells us that y, the UNITS digit of n, must be one greater than x, the TENS digit of n.
So the possible values of n are: 12, 23, 34, 45, 56, 67, 78, and 89
Answer: D
