Data Sufficiency MCQ Set 3

Correct Answer: A

Explanation:

Algebra

First- and second-degree equations

• (1) Since 2 has to be added toy in order to make it equal to *, it can be reasoned that * > y; SUFFICIENT.
• (2) Multiplying both sides of this equation by 2 results in *=2(y -1) or *= 2y - 2. If y were 0, then * would be -2, and y would be greater than *. If y were a negative number like -2, then x = 2(-2) - 2 = -6, and again y would be greater than*. However, if y were a positive number such as 4, then* = 2(4) - 2= 6, and* > y. Since there is no other information concerning the value of y, it cannot be determined if x > j, NOT sufficient.

The correct answer is A; statement 1 alone is sufficient.

Correct Answer: B

Explanation:

Arithmetic Distance problem

A distance problem uses the formula : distance = rate X time.
To find the time, the formula would be rearranged as: time = distance / rate.
To solve this 6 rate problem, it is necessary to know the rate (given here as 70 kilometers per hour) and the distance.

• (1) If D is the distance Paula drove then D >200 and D/70 > 200/70 = 2 6/7 so t > 2 6/7 and t may or may not be less than 3;NOT sufficient.
• If D is the distance Paula drove then D<205 and D/70 < 205/70 = 2 13/14 so t < 2 13/14 <3; SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.

Correct Answer: E

Explanation:

Geometry Coordinate geometry

The *-intercept is the *-coordinate of the point in which the line k crosses the *-axis and would have the coordinates (*,0).

• (1) Knowing the slope of the line does not help in determining the *-intercept, since from point (-5,r) the line k extends in both directions. Without knowing the value of r, the *-intercept could be -5 if r were 0, or it could be other numbers, both positive and negative, depending on the value of r; NOT sufficient.
• (2) Knowing that r > 0 suggests that the *-intercept is not-5; the point (-5,r), where r is a positive number, does lie in quadrant II. It could, however, be any point with an *-coordinate of-5 in that quadrant and line k could have any negative slope, and so the line k would vary with the value of r. Therefore, the *-intercept of line k cannot be determined; NOT sufficient.

Using (1) and (2) together does not help in the determination of the *-intercept, since the point (-5,r) could have any positive jy-coordinate and thus line k could cross the *-axis at many different places.

The correct answer is E; both statements together are still not sufficient.

Correct Answer: D

Explanation:

Arithmetic Interest problem

With simple annual interest, the formula to use is interest = principal x rate X time. It is given that S500 = $5,000 x p/100 x1(year), so p = 10 percent interest.

• (1) If p is 10 percent, then k= 0.8/ is 0.08. Using the same formula, the time is again 1 year; the interest is the same amount; and the rate is 0.08, or 8 percent. Thus, S500 = principal x 0.08 x 1, or principal $6,250; SUFFICIENT.
• (2) If k= 8, then the rate is 8 percent, and the same formula and procedure as above are employed again; SUFFICIENT.

The correct answer is D; each statement alone is sufficient.

Correct Answer: C

Explanation:

Algebra Inequalities

lf x + y/ z > 0, then either one of two cases holds z true. Either (* +y) >0 and z>0, or (*+y) < 0 and z < 0. In other words, in order for the term to be greater than zero, it must be true that either
1) both the numerator and denominator are greater than 0 or 2) both the numerator and denominator are less than 0.

• (1) Regardless of whether (x +y) is positive or negative, the positive or negative value of z must be in agreement with the sign of(x + y in order for x + y/ z > 0. However, there is no information about z here; NOT sufficient.
• (2) If z<0, then (x + y) must be less than 0.However, this statement gives no information about (x + y) NOT sufficient.

This can be solved using (1) and (2) together. From (2), it is known that z < 0, and, going back to the original analysis, for the term to be greater than zero, (x + y) must also be less than 0. If x + y < 0 then x < — y. But x < y from (1) so
x + x < — y + y
2x < 0
x < 0.

The correct answer is C; both statements together are sufficient.

Correct Answer: C

Explanation:

Arithmetic Properties of numbers

• (1) The prime factors of 15 are 3 and 5. So in this case, k has at least 2 different positive prime factors, but it is unknown if there are more positive prime factors; NOT sufficient.
• (2) The prime factors of 10 are 2 and 5, show in g that k has at least these 2 different positive prime factors, but k might or might not have more; NOT sufficient.

Taking (1) and (2) together, since k is divisible by both 10 and 15, it must be divisible by their different positive prime factors of 2, 3, and 5. Thus k has at least 3 different positive prime factors.

The correct answer is C; both statements together are sufficient.