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(1) m and n are even.
(2) gcf (m,n) = 2.
A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements together are sufficient, but NEITHER statement alone is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) together are not sufficient.
A group of people bought $180 worth of theater tickets costing either $10 or $25. How many tickets costing $10 were bought? (1) Fewer than 4 tickets costing $25 were bought (2) More than 10 tickets costing $10 were bought (more)
I have a doubt with this question,
If "fewer than 4" include 0 or not!
How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours (2) If the car’s average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hours less time than it did
Statement 1 - The car traveled the first 200 kilometers in 2.5 hours
Insufficient because the speed of the car may change between 200 and 400 km
Statement 2 -
Assume the average speed of the car for 400 kms be s and time taken be t
s = 400/t (Since speed = distance / time) ... (1)
When time = t - 1, speed = s+20
s + 20 = 400 / (t - 1)
from equation (1)
400/t + 20 = 400 / (t - 1)
400 (t - 1) + 20 t (t - 1) = 400 t
400t - 400 + 20t2 - 20t = 400t
20t2 - 20t - 400 = 0
t2 - t - 20 = 0
t2 - 5t + 4t - 20 = 0
t (t - 5) + 4 (t - 5) = 0
(t - 5) (t + 4) = 0
t = - 5 or t = 4 hours
t = -5 is not possible hence
t = 4 hours
4x+y = 810
22(x+y) = 230
we need to prove x + y = 15
(1) x - y = 9
adding 2y to both sides
x + y = 9 + 2y
since y can be any integer, 9 +2y and x + y can have a many values including 15 (for y = 3)
(2) y/x = 1/4
x = 4y
x + y = 5y
since y can be any integer, 5y and x + y can have a many values including 15 (for y = 3)
x - y = 9
x = 4y
3y = 9
y = 3
x = 12
x + y = 15