students

[ketkoag]

Of the 240 students, 60 are studying both P and T. Is the number of the students who are studying neither of them greater than 140?
1) The number of the students studying P is greater than the students studying T
2) 101 students are studying P.

[SanjeevK]

IMO B
Let the number of students studying P is p and T is t
Let the number of students studying neither is n
so we have 240 - n = p + t - 60
300 - n = p + t
n = 300 - (p + t)
a: p>t. put p = 200, t = 99. n = 1
put p = 60, t = 60. n = 180
insufficient

b: p = 101.
minimum value of t is 60 (since 60 are studying both P and T)
n <= [300-(101+60)]
n <= 139
sufficient

What is the OA

Hope this helps

[Stuart@KaplanGMAT]

Of the 240 students, 60 are studying both P and T. Is the number of the students who are studying neither of them greater than 140?
1) The number of the students studying P is greater than the students studying T
2) 101 students are studying P.

let's try this with less math!

1) P > T

Let's look at two extreme possibilities:

P=61, T=60

and

P = 240, T=60

In the first case, we have 240-61 = 179 people studying neither.

In the second case, we have 240-240 = 0 people studying neither.

Is the number of people studying neither greater than 140? Sometimes yes, sometimes no: insufficient.

2) P = 101

If P = 101, then the maximum number of people who studied neither is 240-101 = 139. Is the number of students who studied neither greater than 140? Definitely not: sufficient.

(2) is sufficient, (1) is not: choose (B)