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GMAT - Data Sufficiency

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 :)

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 + 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

Sufficient.

 

 

Is 4^(x + y) = 8^10? (more)

Is 4x y = 810
(1) x - y = 9
(2) y/x = 1/4

To prove

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)

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

 

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