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# If a and b are integers, what is the value of a+b?

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Math Expert
Joined: 02 Sep 2009
Posts: 53831
If a and b are integers, what is the value of a+b?  [#permalink]

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14 Nov 2016, 03:34
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64% (01:15) correct 36% (01:00) wrong based on 133 sessions

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If a and b are integers, what is the value of a+b?

(1) a·b=1

(2) a/b=1

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Re: If a and b are integers, what is the value of a+b?  [#permalink]

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14 Nov 2016, 03:56
1
Bunuel wrote:
If a and b are integers, what is the value of a+b?

(1) a·b=1

(2) a/b=1

IMO E
Given a and b are integers

From statement 1
a*b= 1 This is possible when both the integers are 1 or -1
1*1=1 or -1*-1=1
a+b can be 2 or -2
hence insufficient

From statement 2
a/b=1 This is satisfied when a=b
a+b can have different values depending on values of a and b
hence insufficient

Combining, a*b=1 and a/b=1
we can say only values to satisfy both conditions is a=1=b and a=-1=b
hence again a+b= 2 or -2
hence insufficient

Hence E
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Re: If a and b are integers, what is the value of a+b?  [#permalink]

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14 Nov 2016, 14:44
Bunuel wrote:

If a and b are integers, what is the value of a+b?

(1) a·b=1

(2) a/b=1

Interpreting statement-1:

(1) Neither a, nor b is '0' (zero).
(2) Both have the same sign; either both of them +ve or both of them -ve.
(3) One is NOT the reciprocal of the other ( as both of them are INTEGERS).
(4) b = 1/a [or a =1/b]
(5) a + b = a + 1/a = ($$a^2$$+1)/a

Therefore, the product of two integers can be 1 in ONLY two possible scenarios, both are +1s or both are -1s.

If both are +ve, a+b =+2 and if both are -ve, then a+b = -2.

CONCLUSION: Can't come to a single value for a+b. Not sufficient.

Interpreting statement-2:
(1) Once again, neither a nor b is '0'.
(2) Both have the same sign; either both of them +ve or both of them -ve.
(3) a = b
(4) a + b = a + a = 2a [or 2b]
(5) The magnitude of the two integers is same.

If x = +5, y = +5; if x = -5 then y = -5 and so on.

CONCLUSION: a+b = could be any +ve or - ve integer. Not sufficient.

Combining both of them:
(1) a+b = a+1/a = (a^2+1)/a (from statement 1)
(2) a+b = a+a = 2a (from statement 2)

(a^2+1)a = 2a
or, a^2+1 = 2a^2
or, a^2 = 1
.:. a = +/- 1
If a = 1, then b = 1 and if a = =1, then b = -1.

a + b = 1+1 = 2, or a + b = -1 -1 = -2.

CONCLUSION: Together the statements are insufficient to come to a single value.

Therefore, IMO, the answer is 'E'.
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Re: If a and b are integers, what is the value of a+b?  [#permalink]

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30 Dec 2017, 12:44
Bunuel wrote:
If a and b are integers, what is the value of a+b?

(1) a·b=1

(2) a/b=1

Statement 1: implies $$a=\frac{1}{b}$$ or $$b=\frac{1}{a}$$. Hence there could be multiple values of $$a$$ & $$b$$. Insufficient

Statement 2: implies $$a=b$$. so $$a+b=2a$$ or $$2b$$. we don't know the value of $$a$$ or $$b$$. Insufficient

Combining 1 & 2: as $$a=b$$ so $$a*b=a^2=b^2=1$$

$$=> a=b=1$$ or $$-1$$. So no unique value. Insufficient

Option E
Re: If a and b are integers, what is the value of a+b?   [#permalink] 30 Dec 2017, 12:44
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