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13 May 2020, 09:02
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Difficulty:
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Question Stats:
48% (02:09) correct
52%
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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.
Are You Up For the Challenge: 700 Level Questions
(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.
Are You Up For the Challenge: 700 Level Questions
13 May 2020, 09:26
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\((a + b)^2 – (a - b)^2 = 4ab\)
Statement 1-
(x+1)*a - x*a = 5
a=5
Unit digit of 4*a*b =20*b is always 0.
Sufficient
Statement 2-
unit digit of b is 0 or 5
unit digit of 4*a*b is again 0.
Sufficient
Statement 1-
(x+1)*a - x*a = 5
a=5
Unit digit of 4*a*b =20*b is always 0.
Sufficient
Statement 2-
unit digit of b is 0 or 5
unit digit of 4*a*b is again 0.
Sufficient
Bunuel
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.
Are You Up For the Challenge: 700 Level Questions
(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.
Are You Up For the Challenge: 700 Level Questions
14 May 2020, 01:00
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Bunuel
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.
Are You Up For the Challenge: 700 Level Questions
(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.
Are You Up For the Challenge: 700 Level Questions
Solution
Step 1: Analyse Question Stem
- • a and b are non-negative integer.
• We need to find the unit’s digit of \((a+b)^2 – (a -b)^2\)
- o Now, \((a+b)^2 – (a -b)^2 = a^2 + b^2 +2*a*b – (a^2 + b^2 – 2*a*b) = 4*a*b\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The difference between any two consecutive multiples of a is 5
- • It means a is a multiple of 5.
- o So, unit’s digit of a can be either 0 or 5
- o So, unit’s digit of 4*a*b = 4*0* unit’s digit of b = 0
o Or, unit’s digit of 4*a*b =4*5*unit’s digit of b = 0* unit’s digit of b = 0
Statement 2: b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
- • Thus, unit’s digit of b can be 0 or 5.
• So, unit’s digit of 4*a*b = 4*unit’s digit of a* units digit of b
- o So, unit’s digit of 4*a*b = 4* unit’s digit of a*0 = 0
o Or, unit’s digit of 4*a*b =4*unit’s digit of a*5 = 0* unit’s digit of a = 0
