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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 13 May 2020, 09:02
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75% (hard)

Question Stats:

47% (02:08) correct 53% (02:22) wrong based on 91 sessions

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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.


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D
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 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



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
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 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
Show more

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, \((a+b)^2 – (a -b)^2 = a^2 + b^2 +2*a*b – (a^2 + b^2 – 2*a*b) = 4*a*b\)
So basically, we need to find the unit’s digit of 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
    • So, unit’s digit of 4*a*b = 4*unit’s digit of 5k* unit's digit of b
      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
    • Therefore, irrespective of unit’s digit of b, the units’ digit of 4*a*b will always be 0.
Hence, statement 1 is sufficient and we can eliminate answer option 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.
    • 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
    • Therefore, irrespective of unit’s digit of a, the units’ digit of 4*a*b will always be 0.
Hence, statement 2 is also sufficient and the correct answer is Option D.
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 17 May 2020, 08:47
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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

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, \((a+b)^2 – (a -b)^2 = a^2 + b^2 +2*a*b – (a^2 + b^2 – 2*a*b) = 4*a*b\)
So basically, we need to find the unit’s digit of 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
    • So, unit’s digit of 4*a*b = 4*unit’s digit of 5k* unit's digit of b
      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
    • Therefore, irrespective of unit’s digit of b, the units’ digit of 4*a*b will always be 0.
Hence, statement 1 is sufficient and we can eliminate answer option 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.
    • 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
    • Therefore, irrespective of unit’s digit of a, the units’ digit of 4*a*b will always be 0.
Hence, statement 2 is also sufficient and the correct answer is Option D.
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Hi Team,

Could you please elaborate statement 2

we can take b as 65 and even integer as 22 in that case unit digit will not be same.

I want to know how you determined that b should have unit digit as 0 or 5.
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 17 May 2020, 10:03
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According to statement 2-

Unit digit of results will remain same. It doesn't say unit digit of b will be same as that of result.

For example - 65*22= xyz0; 65*44=abc0 (always ends with 0)



vishumangal
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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

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, \((a+b)^2 – (a -b)^2 = a^2 + b^2 +2*a*b – (a^2 + b^2 – 2*a*b) = 4*a*b\)
So basically, we need to find the unit’s digit of 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
    • So, unit’s digit of 4*a*b = 4*unit’s digit of 5k* unit's digit of b
      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
    • Therefore, irrespective of unit’s digit of b, the units’ digit of 4*a*b will always be 0.
Hence, statement 1 is sufficient and we can eliminate answer option 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.
    • 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
    • Therefore, irrespective of unit’s digit of a, the units’ digit of 4*a*b will always be 0.
Hence, statement 2 is also sufficient and the correct answer is Option D.


Hi Team,

Could you please elaborate statement 2

we can take b as 65 and even integer as 22 in that case unit digit will not be same.

I want to know how you determined that b should have unit digit as 0 or 5.
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What is the units digit of (a + b)^2 – (a - b)^2, where a and b are no 11 Jan 2023, 10:43
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