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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If two 2-digit positive integers have their respective tens digits exc
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11 Apr 2022, 03:29
11 Apr 2022, 03:29
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If two 2-digit positive integers have their respective tens digits exchanged, the difference between the pair of integers changes by 4. What is the greatest possible difference between the original pair of integers?
A) 76
B) 80
C) 82
D) 90
E) 94
A) 76
B) 80
C) 82
D) 90
E) 94
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If two 2-digit positive integers have their respective tens digits exc
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14 Apr 2022, 02:29
14 Apr 2022, 02:29
Expert Reply
The maximum possible difference between two 2-digit positive integers is obtained when one integer is in 90s and other is in 10s i.e one of the integer has 9 at ten's place and other has 1 at ten's place.
Let x be the unit's digit of 1 integer and y be the unit's digit of other.
So, our numbers are 90+x and 10+y
Let m be the difference between these two integers.
Then,
\(90+x - (10+y)=m\)
or \(80+x-y=m\)
or \(x-y=m-80\) .......(1)
Now, the integers have their respective ten's digits exchanged. So, the new numbers are 10+x and 90+y.
It is given that the difference changes by 4. To maximize the difference of original numbers, the new difference should reduce by 4. So, our new difference is m-4
\(90+y-(10-x)=m-4\)
or \(80+y-x=m-4\)
or \(y-x=m-84\)
or \(x-y=84-m\) ........(2)
From 1 and 2 we have,
\(m-80=84-m\)
or \(2m=164\)
or \(m=82\)
Answer: C
Let x be the unit's digit of 1 integer and y be the unit's digit of other.
So, our numbers are 90+x and 10+y
Let m be the difference between these two integers.
Then,
\(90+x - (10+y)=m\)
or \(80+x-y=m\)
or \(x-y=m-80\) .......(1)
Now, the integers have their respective ten's digits exchanged. So, the new numbers are 10+x and 90+y.
It is given that the difference changes by 4. To maximize the difference of original numbers, the new difference should reduce by 4. So, our new difference is m-4
\(90+y-(10-x)=m-4\)
or \(80+y-x=m-4\)
or \(y-x=m-84\)
or \(x-y=84-m\) ........(2)
From 1 and 2 we have,
\(m-80=84-m\)
or \(2m=164\)
or \(m=82\)
Answer: C
gmatclubot
Re: If two 2-digit positive integers have their respective tens digits exc [#permalink]
14 Apr 2022, 02:29
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