DS-Prob 3

[er.twi.fb]

1.How many integers, x, satisfy the inequality b < x < a?
1) a - b = 78
2) a > 100 and b < 50

[Haaress]

How many integers, x, satisfy the inequality b < x < a?
1) a - b = 78
2) a > 100 and b < 50

In the inequality, the range of x is valid from b+1 through a - 1 inclusive.

Stmt 1 provides the number of integers between b and a , and this can provide the exact number of integers between b and a as follows ( you do not need to do this calc)

(a-1) - (b+1) +1 = (a -b) -1 , but a - b is 78 ,thus 78 - 1 = 77. so the number of integers between b and a is 77.

Stmt 2. Is insuff since the values of both a and b can vary.

Thus the answer is A.

Edited for spelling.

[sk818020]

Haaress is correct.

Simply from a logical stand point.

1) a-b=78

No matter whether a or b, or both are negative or positive this equation always gives you the amount of numbers between a and b. This definitely lets you answer how many numbers satisfy the given equation.

2) a>100 and b<50

This information alone simply tells you that there are an infinite amount of different numbers that a and b could be. You could never determine the number of spaces between a and b by this information alone.

Hope this helps.

Thanks,

Jared

[Rahul@gurome]

1.How many integers, x, satisfy the inequality b < x < a?
1) a - b = 78
2) a > 100 and b < 50

(1) If a = 78 and b = 0 then a - b = 78 and 0 < x < 78, which implies there will be 77 integers between a and b.
It is not given in the question that a and b are integers, so a = 78.5 and b = 0.5, so that a - b = 78 and 0.5 < x < 78.5, which implies there are 78 integers between a and b.
So, there is no unique answer.

Hence, (1) is NOT SUFFICIENT.

(2) If a = 101 and b = 49 then 49 < x < 101 implies x = 51
If a = 110 and b = 45 then 45 < x < 110 implies x = 64
So, there is no unique answer.

Hence, (2) is NOT SUFFICIENT.

Combining (1) and (2), a and b can take any values so that a - b = 78, so again we have a number of possible solutions.

The correct answer is (E).