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

Question

If a and b are integers, what is the value of a + b ?
 
(1) 493 < a < b < 498
 
(2) 494 < a < b < 497

tallyho_88 · Answer

ANS- B
a and b are integers, so fractions are out. 
Statement I-with the range mentioned a and b can have multiple values.- not sufficient.
Statement II- with the range mentioned (and since b is larger than a), there can only be one set of values that satisfy this equation- i.e. b=496 and a=495.- sufficient.

adiagr · Answer

Statement 1

It is given that a and b are integers and 493 < a < b < 498

available values are 494, 495, 496 and 497. b can have values 495, 496 and 497 and a can have values 494, 495, 496

(1) is not sufficient

Statement 2

It is given that a and b are integers and 494 < a < b < 497

Available integer values are 495 and 496.

since a will have to be 495 and b will have to be 496.

Statement (2) is Sufficient

Answer: B

max0010 · Answer

I would go with E.

Since non of the options tell if a=b

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MathRevolution · Answer

There are 2 variables in the original condition (a and b). In order to match the number of equations and the variables, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and the condition 2) at the same time, C is the correct answer. However, this is an integer question, one of the key questions. Hence, we can apply the Common Mistake Type 4(A). Using the condition 2) alone, we get a=495 and b=496. The answer is unique and the condition is sufficient. The correct answer is B. Hence, if C and B are both the answers, B is the correct answer.

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rhine29388 · Answer

Statement 1 tells us 493 < a < b < 498
As per this statement a can be 494,495,496 whereas b can be 495,496,497.Following the condition a<b, we get different values a+b depending upon which values we choose so insufficient
Statement 2 tells us 494 < a < b < 497
As per this statement a can be only 495 and b can be only 496. so we get a definite value for a+b. So sufficient
Correct Answer - B

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

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