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16 Jan 2023, 11:15
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D
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Difficulty:
85%
(hard)
Question Stats:
45% (02:31) correct
55%
(01:48)
wrong
based on 47
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are non-negative integers?
(1) The difference between any two consecutive multiples of a is 5.
(2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
(1) The difference between any two consecutive multiples of a is 5.
(2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
16 Jan 2023, 14:39
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Bunuel
\((a + b)^2 – (a - b)^2 = 4ab\)
Statement 1
(1) The difference between any two consecutive multiples of a is 5.
This statement means a = 5
The difference between two consecutive multiples of a number is the number itself.
For example, the difference between any two consecutive multiples of 2 is 2.
4ab = 4 * 5 * b , the unit digit is 0.
The statement is sufficient.
Statement 2
(2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
If the unit digit of b is 0, multiplying any even integer will result in an unit digit of 0
Also if the unit digit of b is 5, multiplying any even integer will result in an unit digit of 0.
So we can conclude that b has 0 or 5 in its unit digit.
In both the cases, the unit digit of 4*a*b = 0.
Sufficient.
Option D
17 Jan 2023, 00:01
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Bunuel
Solution:
Pre Analysis:
- We are given \((a + b)^2 – (a - b)^2\)
\(⇒a^2+b^2+2ab-(a^2+b^2-2ab)\)
\(⇒a^2+b^2+2ab-a^2-b^2+2ab\)
\(⇒4ab\) - We are asked the unit digit of \(4ab\)
Statement 1: The difference between any two consecutive multiples of a is 5
- From this statement, we can infer that \(a=5\)
- Becasue the difference between any two consecutive multiples of 5 is 5
- Thus, the unit digit of \((4ab)_u=(4\times 5\times b)_u=0\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b
- From this statement, we can infer that \(b=0\) or \(b=5\)
- Thus, the unit digit of \((4ab)_u=(4\times a\times 5)_u=(4\times a\times 0)_u=0\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
