Test: Data Sufficiency- 2 - GMAT MCQ

From statement I:

The angle bisector of angle A divides the opposite side in ratio 2:3. Knowing this, length of side AC cannot be found.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

The length of side AB is 12 cm. Knowing length of side AB, length of side AC cannot be found.

∴ Statement II alone is not sufficient to answer the question.

From statements I and II together:

The length of side AB is 12 cm. The angle bisector of angle A divides the opposite side in ratio 2:3. So, ratio of sides containing angle A will be 2:3. But it cannot be said whether, AB:AC = 2:3 or AC:AB = 2:3.

Using the value of length of side AB, we get different lengths of side AC in two cases.

∴The length of side AC cannot be uniquely found.

∴ Even using both the statements together, we cannot answer the given question.

Time taken = change in time = 30 minutes = 1/2 hours
In statement 1, Initial velocity (v₁) = 20 miles per hour and change in time = 0.5 hours (given)
Final velocity (v₂) = 25 miles per hour.
Acceleration = (v₂ - v₁)/ change in time = (25 - 20)/ 0.5 = 10 miles per hour per hour. Therefore, the statement is sufficient.
In statement 2, Change in velocity = 5 miles per hour and change in time = 0.5 hours (given).
Acceleration = Change in velocity/change in time = 5/0.5 =10 miles per hour per hour. Therefore, the statement is sufficient.
Therefore, EACH statement ALONE is sufficient.

Parallel lines have equal slopes.
In statement 1, if both lines are in the first, second and fourth quadrant then they have a negative slope. This alone is not enough to prove that they are parallel or not, hence, the statement is insufficient.
In statement 2, the y intercepts are 8 and 4 to imply that the equation are of the form y = mx + 8 and y = bx + 4. But this does not enough to determine if the lines area parallel since, notheing is said about the value of m and b, hence, the statement too is insufficient.
Combining the two statements, we have equations having negative gradients, thus, y =-mx + 8 and y = -bx + 4. Since we are not sure of -m = -b, we cannot say that they are parallel on not. Therefore,  Statements (1) and (2) TOGETHER are NOT sufficient.

Since s, p and q are interior angles of Isosceles triangle, s + p + q = 180°.
In statement 1, If s = 72°, then p + q + 72 = 180° and
p + q = 180°.
Since we have two unknowns in one equation and we are not sure which angles are base angles, we cannot determine the value of q, hence the statement is not sufficient.
In statement 2, p and q are base angles of the triangle, hence from s + p + q = 180°, we have s + 2q = 180°, but p = q.
But the statement is not sufficient since it does not have any information about s.
Combining the two, we have s + 2q = 180° and s = 72°, we have
72° + 2q = 180°; 2q = 180 - 72 = 108°. q = 54°.
Therefore,  BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

An obtuse angle is an angle more than 90° and less than 180°.
In statement 1, A is more than 90°. This implies that A can be as well take a value more than 180° to be a reflex angle or between 90° and 180° to be an obtuse angle. Therefore, the statement is not sufficient.
In statement 2, if B is an acute angle, let B = 45, then A will be its supplement, that is, A = 180° - 45 = 135° an obtuse angle. This is true for all values of B taken. Hence statement B is sufficient.

In statement1, k and m lie on a straight line hence k + m =180°. Since m is unknown, the statement is insufficient.
In statement 2, m = 39°; since there is no relationship between m and k, we cannot find the value of k. Thus the statement is not sufficient.
Combining the two statements, we have k + m = 180°, and m = 39°.
Substituting for m, we have k + 39 = 180, k = 141°. Thus, BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

The line L passes through (2,8) and (0,0) hence its slope is
slope = (8 - 0)/(2 - 0) = 4.
Since L is perpendicular to the line in question, the product of their slope is -1. Therefore, the slope of the line in question is -1/4.
In statement 1, the line passes the origin, (0,0) and its slope is -1/4 hence its equation is y = -x/4. The statement is sufficient.
In statement 2, line passes through the (2,0.5) and its slope is -1/4. Thus we have (y + 0.5)/(x - 2) = -1/4
y + 1/2 = -x/4 + 1/2
thus  y = -x/4. The statement is sufficient too.
Thus, EACH statement ALONE is sufficient.

The capacity of cistern is 15 cubic feet.
In statement 1, let the second pipe supply water a rate of x feet per minute. The rate of the first pipe is 3x feet per minute. Thus, the statement is insufficient.
In statement 2, the pipes fill 8 cubic feet in 10 minute. Therefore, 15 cubic feet will be filled in (15 × 10)/8 = 18.75 minutes. Hence, the statement is sufficient.

2x + 1 > 0
In statement 1, a is an integer, when x = -2, 2x + 1 = -3 < 0. When x = 2, 2x + 1 = 5 > 0, hence the statement is not sufficient.
In statement 2, |x| < 1.5 implies that -1.5 < x < 1.5.
When x = 1.4, 2x + 1 = 3.8 > 0. When x = -1.4, 2x + 1 = -1.8 < 0.
Hence, the statement is not sufficient.
Combining the two statements, we have, x, an integer and -1.5 < x < 1.5, considering the more strict condition, -1.5 < x < 1.5, we find that 2x + 1 < 0, when x = -1.4 and 2x + 1 > 0 when x = 1.4.
Therefore, Statements (1) and (2) TOGETHER are NOT sufficient.

We consider 12 and t.
In statement 1, the Least Common multiple of 12 and t is 48 to mean that t is a factor of 48. This mean that, t can take 16, 24 and 48. Hence the statement is not sufficient.
In statement 2, the Greatest Common divisor is 4. Therefore, t can take 4, 8, 16, 28, 32, 40 among others. Thus, the statement is not sufficient.
Combining statements 1and 2, we have 16 featuring in both lists, hence it satisfies the two conditions. Therefore, t =16. Thus BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.