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21 Feb 2019, 00:30
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D
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Difficulty:
35%
(medium)
Question Stats:
74% (02:09) correct
26%
(02:15)
wrong
based on 125
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A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
A. 8
B. 6
C. 4
D. 2
E. 1
A. 8
B. 6
C. 4
D. 2
E. 1
21 Feb 2019, 10:11
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Bunuel
A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
A. 8
B. 6
C. 4
D. 2
E. 1
A. 8
B. 6
C. 4
D. 2
E. 1
given
100a+10b=10x
or say
10a+b=x
now
error done makes
it
90a+9b+10b+a=(x-1.8)*10
or say
91a+19b= 10x-18
so
91a+19b=100a+10b-18
or say
9a-9b=18
a-b=2
IMO D
22 May 2019, 20:56
Kudos
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Bunuel
A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
A. 8
B. 6
C. 4
D. 2
E. 1
A. 8
B. 6
C. 4
D. 2
E. 1
I think my method is correct. Please correct me if I'm wrong.
\(\frac{Sum of 10 Positive Integers}{10} = X\) <------ Average #1
Sum of 10 Positive Integers = \(X(10)\) <------ Sum #1
\(\frac{Sum of 10 Positive Integers}{10} = (X - 1.8)\) <------ Average #2 with reversed digits.
Sum of 10 Positive Integers = \(10(X - 1.8)\) <------ Sum #2
Sum of 10 Positive Integers = \(10X - 18\)
Sum differences:
= [Sum #2] - [Sum #1]
= (10X - 18) - 10X
= 10X - 18- 10X
= -18
Now start taking the lowest double digit numbers and subtracting from their reversed counterparts.
10: 10 - 01 = 9 <---- Nope
11: 11 - 11 = 0 <---- Nope
12: 12 - 21 = -9 <---- Nope
13: 13 - 31 = -18 <---- YASS!!!
The difference between digits is (3 - 1) = 2
24: 24 - 42 = -18 <---- YASS!!!
The difference between digits is (4 - 2) = 2
35: 35 - 53 = -18 <---- YASS!!!
The difference between digits is (5 - 3) = 2
46: 46 - 64 = -18 <---- YASS!!!
The difference between digits is (6 - 4) = 2
Answer: D
