Test: Data Sufficiency - 2 - GMAT MCQ

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.

Answer: Statement 2 alone is sufficient to answer the question; Statement 1 alone is not sufficient.

Explanation:

Statement 1: The first pipe's rate is three times that of the second pipe. This provides a ratio but no actual flow rates. Without knowing an actual flow rate, we cannot calculate the time needed to fill the cistern. Therefore, Statement 1 alone is insufficient.

Statement 2: The two pipes together fill 8 cubic feet in 10 minutes. This allows us to calculate their combined flow rate:

Combined flow rate = Volume/Time = 8 cubic feet/10 minutes = 0.8 cubic feet per minute

Knowing the cistern's total capacity (15 cubic feet) and the combined flow rate, we can find the time to fill the cistern:

Time to fill cistern = Total volume/Combined flow rate = 15/0.8 = 18.75 minutes

Therefore, Statement 2 alone is sufficient to answer the question.

Combined Statements: While Statement 1 provides the ratio of the pipes' flow rates, combining it with Statement 2 isn't necessary since Statement 2 already gives us enough information to solve the problem.

Conclusion: Only Statement 2 is needed to determine how long it takes the two pipes to fill the cistern. Statement 1 alone is insufficient, and combining both statements isn't required.

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.

Step 1: Key Data from the Question 

Set S has 6 elements.
The elements of set S are distinct.
x and y are prime numbers. Because 2 is already an element in S, both x and y have to be odd.
0 < x < 40 and 0 < y < 40

Step 2: Check Statement I

I. The maximum possible range of the set is greater than 33.
The keyword in this entire statement is maximum. We have to determine whether the maximum value possible for the range exceeds 33.
We know x and y are prime numbers. The largest prime number less than 40 is 37.
If either x or y is 37, the largest number in the set will be 37 and the smallest number is 2.
Therefore, the maximum range of the set will be 37 - 2 = 35. It is greater than 33.

Statement I is true. So, eliminate choices that do not contain I.
Eliminate choice D

Step 3: Check Statement II

II. The median can never be an even number.
There are 6 numbers in the set. Therefore, the median is the arithmetic mean of the 3rd and the 4th term when the numbers are written in ascending or descending order.
The elements are {2, 4, 6, 8, x, y}, where x and y are prime numbers.
If x and y take 3 and 5 as values, the median is 4.5
If x = 3, y = 7 or greater, the median is 5.
If x = 5, y = 7 or greater, the median is 5.5
If x = 7, y = 11 or greater, the median is 6.5
If x = 11 or greater and y = 13 or greater, the median is 7.
It is quite clear that the median is either an odd number or is not an interger. So, the median can never be an even integer.

Statement II is true. Eliminate choices that do not contain II.
Eliminate choices A and C as well.

Step 4: Check Statement III

III. If y = 37, the average of the set will be greater than the median.
If y = 37, the set will be {2, 4, 6, 8, x, 37}, where x is a prime number greater than 2 and less than 37.
The average will be 57 + x657 + x6 = 9.5 + x6x6
If x = 3, median = 5 and average = 10. Average > median.
If x = 5, median = 5.5 and average = 10.33. Average > median
If x = 7, median = 6.5 and average = 10.66. Average > medain
If x = 11 or greater, the median = 7. Average will be definitely greater than 10. So, Average > Median.
It is true that the average is greater than the median if y = 37.

Statement III is also true.
Statements I, II, and III are true.

Choice C is the correct answer.