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# If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6

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If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 20:23
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If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?

(1) m is 82 greater than the tens digit of m.
(2) n is 18 greater than the tens digit of n.

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 21:07
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If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?

There is a relationship between m and n in main statement and then in each statement, so both should be sufficient.
m=10a+b and n=10b+a

(1) m is 82 greater than the tens digit of m.
So m=82+a......10a+b=82+a.....9a=82-b
a as 9 gives b as 1....m=91
a as 2 will give b as 10, a 2-digit number... Not possible
Sufficient

(2) n is 18 greater than the tens digit of n.
n=18+b........10b+a=18+b......9b=18-a
Only value of b is 1 for both a and b to be single digit.
Number n=19
Sufficient

D
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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 21:21
1
Let m=xy, then n=yx. We are to determine m. The given condition is that m and n are two-digit numbers.

Statement 1: m is 82 greater than the tens digit of m
Sufficient. Statement 1 tells us that m > 90 since only a value greater than 90 will yield a difference between itself and it's tens digit to be 82.
With this information in mind, we can narrow down to 91 as the value of m, since it is the only value greater than 90 that yields a difference of 82 when 9 is taken out of it.

Statement 2: n is 18 greater than the tens digit of n.
Sufficient. Statement 2 tells us that m<21, since only a value less than 21 will yield a difference between itself and it's tens digit to be 19. Two values less than 21 satisfy the given condition in statement 2: 19 and 20. The reverse of 19 is 91, which is a two-digit number, but the reverse of 20 is 2, which is not a two-digit number. We can, therefore, discard 20 as n, and conclude that n=19. This further implies that m=91.

Both statements are sufficient on their own to determine the value of m.

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 22:02
1
let m = 10a + b
n=10b + a

evaluating option A:

m= 82+ a
10a+b = 82+ a
9a +b= 82

a and b are positive integers therefore
possible values of a,b:
a= 9, b=1
a=8, b=10--- not possible

therefore a=9 and b=1
m=91
A is sufficient!

Evaluating B:

n= 18+ b
10b+a= 18+b
9b+a = 18

a, b are positive integers less than 10
possible values of a,b

b=1, a=9
b=2, a=0- not possible as m would not be a two digit integer

therefore n=19 and m=91

B is sufficient

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 22:32
m = 10x+y
n = 10y + x

Q: Find the value of m.

Statement 1: m is 82 greater than the tens digit of m.

m = x + 82.
Substituting this in the eqn. for m,

x+82 = 10x + y
9x + y = 82

We cannot find the value of m from this.
Hence, Statement 1 is INSUFFICIENT. AD/BCE

Statement 2: n is 18 greater than the tens digit of n.

n = y + 18
Substituting this in the eqn. for n,

y+18 = 10y + x
x+9y = 18

We cannot find the value of n from this.
Hence, Statement 2 is INSUFFICIENT. AD/BCE

Statement 1 and 2 together:

Combining both the eqn.,

9x + y = 82
x+9y = 18

We know that we can find the value for x and y. Therefore we can find the value for m also.

Hence Statements 1 and 2 together are SUFFICIENT.

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 23:08
Let's assume m = AB, n = BA

1) m = A + 82 = 10A + B, not sufficient enough

2) n = B + 18 = 10B + A, again not sufficient enough.

1 & 2) m - n = A-B + 82-18 = 9(A-B)

=> 8(A-B) = 64
=> A - B = 8
=> if A = 8, B = 0 and m = 80, n = 8 (this is not possible as both are 2 digit integers)
Also another possibility is,
If A = 9, B = 1 and m = 91, n = 19. This satisfies all the criterias mentioned.

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 23:14
1
If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?

(1) m is 82 greater than the tens digit of m.
Let m = 10a + b
Now 10a + b - a = 82
9a + b = 82
Since both a and b are such that a = 9 and b = 1, above equation suggests that a > b possibly 'a' being maximum and 'b' being minimum.
After checking, only for a = 9 and b = 1 satisfy the given condition.
Hence m = 91 where 91 - 9 = 82

SUFFICIENT.

(2) n is 18 greater than the tens digit of n.
Let n = 10b + a
Now, 10b + a - b = 18
9b + a = 18
Since both a and b are such that a = 0, 9 and 1 ≤ b ≤ 2, above equation suggests that possible solutions are for a = 0 and b = 2 OR a = 9 and b = 1.
After checking, both n = 20 and n = 19 satisfy the given condition.
So m = 91, since m being a two digit number m = 2 is not possible.

SUFFICIENT.

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 23:22
IMO: B
Lets say:
n=ab=10a+b
m=ba=10b+a

m=?

1)m=82+b
10b+a=82+b
9b+a=82
if b=1, a=73;b=2, a=64 and so on. Not Sufficient
2)n=a+18
10a+b=a+18
9a+b=18
Only one set satisfies the above equation: a=1 and b=9. Therefore, m=91. Sufficient
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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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28 Oct 2019, 23:23
1
m =xy (two-digit integer)
n= yx (two-digit integer) —> with reversed integer .

—> xy = 10x+ y
—> yx= 10y+ x

(Statement1):
10x+ y = x+82
9x+ y = 82
(x and y —> 1,2....8,9)
—> in order y to be integer from 1 to 9, x must be only equal to 9.
( if x= 8, then y will be equal to 10, —> y cannot be 10.)

Well, x should be 91.
Sufficient

(Statement2):
10y+ x = y+18
9y+ x= 18
—> in order x to be integer number from 1 to 9, y should be only equal to 1.( if y=2, then x will be zero(0). —> x cannot be zero(0).

Well n should be 19–> m will be equal to 91.

Sufficient

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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29 Oct 2019, 02:47
(1) m is 82 greater than the tens digit of m.

Possible values for tens digit of m and m are

1.....83
2.....84
3.....85
.
.
.
8....90....Not possible since n is 2 digit number....
9....91

So clearly insufficient

(2) n is 18 greater than the tens digit of n....Clearly insufficient...Since we will get 9 possible vales as above..

Combining both we will get...

m=91
n=19

OA:C

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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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29 Oct 2019, 06:03
Let m = xy —> n = yx
—> Value of m = 10x + y and n = 10y + x

(1) m is 82 greater than the tens digit of m.
—> 10x + y - x = 82
—> 9x + y = 82

Possible values of (x, y) = (9, 1) ONLY
—> m = 91 —> Sufficient

(2) n is 18 greater than the tens digit of n.
—> 10y + x - y = 18
—> 9y + x = 18

Possible values of (x, y) = (9, 1) ONLY
—> m = 91 —> Sufficient

IMO Option D

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If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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Updated on: 04 Nov 2019, 04:48
#1

m is 82 greater than the tens digit of m.
m=91 and 91-9 ; 82
sufficient
#2
n is 18 greater than the tens digit of n.
(10B+A)-B=18
(A,B)=(1,9)
9(1)+(9)=18
sufficeint
IMO D

If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?

(1) m is 82 greater than the tens digit of m.
(2) n is 18 greater than the tens digit of n.

Originally posted by Archit3110 on 29 Oct 2019, 07:43.
Last edited by Archit3110 on 04 Nov 2019, 04:48, edited 1 time in total.
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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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29 Oct 2019, 18:40
1

Statement 1: Sufficient
Since M is a two digit integer (10-99) and 82 greater than its tens digit (a positive integer 1-9), M must be greater than 82. So, Tens digit of M CAN be 8 or 9.
If Tens digit of M is 8, M=8+82=90. So, N will be 09 (one digit) which is not possible because N is TWO digit integer. So, Tens digit of M CAN NOT BE 8.
If Tens digit of M is 9, M=9+82=91. So, N will be 91, a TWO digit integer. So, Tens digit of M Must BE 9 and M=91

Statement 2: Sufficient
Since the tens digit of N is 1-9, N must be 19-27. So, the tens digit of N is either 1 or 2.
If Tens digit of N is 2, N=2+18=20. So, M will be 02 (one digit) which is not possible because M is TWO digit integer. So, Tens digit of N CAN NOT BE 2.
If Tens digit of N is 1, N=1+18=19. So, M will be 91, a TWO digit integer. So, Tens digit of N Must BE 1 and N=19 and M=91
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Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6  [#permalink]

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04 Nov 2019, 04:24
Quote:
If m and n are two two-digit positive integers with reversed digits (e.g 26 and 62 are 2 two-digit integers with reversed digits), what is the value of m?

(1) m is 82 greater than the tens digit of m.
(2) n is 18 greater than the tens digit of n.

(m,n) = 2-digit positive integers
m = 10A+B
n = 10B+A
1≤(A,B)≤9

(1) m is 82 greater than the tens digit of m. sufic.

(10A+B)-A=82…9A+B=82…(1≤(A,B)≤9)…(A,B)=(9,1)…9(9)+(1)=82

(2) n is 18 greater than the tens digit of n. sufic.

(10B+A)-B=18…9B+A=18…(1≤(A,B)≤9)…(A,B)=(1,9)…9(1)+(9)=18

Re: If m and n are two 2-Digit integers with reversed digits (e.g 26 and 6   [#permalink] 04 Nov 2019, 04:24
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