GMAT - Data Sufficiency
PerlaLyonela 5 months ago Data Sufficiency | Number Theory
If x=6m^2 + 4n^2, what is the greatest even number that must be a factor of x? (more)
(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.
If m equals to n, then the expression becomes 10m^2. Since both statements mean that 2 is factor . The greatest factor would be 20. Correct me if I am wrong :)
Prateek Jain 5 months ago Data Sufficiency | Arithmetic | Linear equations
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!
S E 8 months ago Data Sufficiency |
Data Sufficiency (more)
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 + 20t^{2} - 20t = 400t
20t^{2} - 20t - 400 = 0
t^{2} - t - 20 = 0
t^{2} - 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
Sufficient.
LEAP Administrator 9 months ago Data Sufficiency | Exponents
Is 4^(x + y) = 8^10? (more)
Is 4^{x y} = 8^{10}
(1) x - y = 9
(2) y/x = 1/4
To prove
4^{x+y} = 8^{10}
2^{2(x+y)} = 2^{30}
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)
Insufficient
(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)
Insufficient
Combining both
x - y = 9
x = 4y
subsituting
3y = 9
y = 3
x = 12
x + y = 15
sufficient
LEAP Administrator 9 months ago Data Sufficiency | Inequalities
Statement 1
n > 2
since 1/10 < 1 the sign of inequality will change because (1/10)^{x} is a decreasing function
(1/10)^{n} < (1/10)^{2}
(1/10)^{n} < 0.01
sufficient
Statement 2
(1/10)^{n-1} < 0.1
(1/10)^{n} * (1/10)^{-1} < 0.1
(1/10)^{n} * 10 < 0.1
(1/10)^{n} < 0.01
sufficient