Data Sufficiency MCQ Set 2

Correct Answer: D

Explanation:

Arithmetic Statistics

In determining the standard deviation, the difference between each measurement and the mean is squared, and then the squared differences are added and divided by the number of measurements. The quotient is the variance and the positive square root of the variance is the standard deviation.

• (1) If the variance is 4, then the standard deviation = √4 = 2, which is less than 3; SUFFICIENT.
• (2) For each measurement, the difference between the mean and that measurement is 2. Therefore, the square of each difference is 4, and the sum of all the squares is 4 X 20 = 80.
  The standard deviation is √ 80/20 = √4 = 2, which is less than 3; SUFFICIENT.

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

Correct Answer: C

Explanation:

Arithmetic Statistics

The range of a set of integers is equal to the difference between the largest integer and the smallest integer. The range of the set of integers 3, 4, 5, and 6 is 3, which is derived from 6-3.

• (1) Although it is known that y > 3x, the value of* is unknown. If, for example,* = 1, then the value of y would be greater than 3. However, if * = 2, then the value of y would be greater than 6, and, since 6 would no longer be the largest integer, the range would be affected. Because the actual values of * and y are unknown, the value of the range is also unknown; NOT sufficient.
• (2) If * > 3 and y > x, then * could be 4 and y could be 5. Then the range of the 6 integers would still be 6 - 3 or 3. However, if * were 4 and y were 15, then the range of the 6 integers would be 15-3, or 12. There is no means to establish the values of* and y, beyond the fact that they both are greater than 3; NOT sufficient.

Taking (1) and (2) together, it is known that * > 3 and that y > 3*. Since the smallest integer that x could be is thus 4, then y >3(4) or y >12. Therefore, the integer y must be 13 or larger. When y is equal to 13, the range of the 6 integers is 13- 3 = 10, which is larger than 9. As y increases in value, the value of the range will also increase.

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

Correct Answer: D

Explanation:

Algebra Inequalities

Note that x^r+s =(x^r)(x^s).

• (1) If 5* < 1, then 5 ^{x + 2} / 25 <1 since
  5^{x + 2} / 25 = 5^x . 5²/ 25 = 5^x : Sufficient
• (2) If* <0, then
  * + 2 < 2 : add 2 to both sides
  5^{x + 2} < 5² because a < b implies 5 ^a < 5 ^b
  5^{x + 2} / 25 < 1: divide both sides by5² = 25: SUFFICIENT.

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

Correct Answer: C

Explanation:

Arithmetic Percents

The surveyed companies could be placed into one of the following four categories:

1. Requiring computer skills and requiring writing skills
2. Requiring computer skills but not requiring writing skills
3. Not requiring computer skills but requiring writing skills
4. Not requiring either computer skills or writing skills

It is given that 20 percent of the surveyed companies fell into category 1. It is necessary to determine what percent of the surveyed companies fell into category 4.

• (1) This helps identify the percentage in category 2. Since -4 the companies that required computer skills also required writing skills (i.e., those in category 1), then the other -= of the companies that required computer skills did not require writing skills (thus category 2 = category 1). However, this information only establishes that 20 percent required computer skills, but not writing skills; NOT sufficient.
• (2) While this establishes category 3, that is, that 45 percent required writing skills but not computer skills, no further information is available; NOT sufficient.

Taking (1) and (2) together, the first three categories add up to 85 percent (20 +20+45). Therefore, category 4 would be equal to 100- 85= 15 percent of the surveyed companies required neither computer skills nor writing skills.

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

Correct Answer: D

Explanation:

Algebra

First- and second-degree equations

• (1) If 3q is added to both sides of this equation, it can be rewritten as 3w+ 3q= 3.When each term is then divided by 3, it yields w + q = 1 ; SUFFICIENT.
• (2) When each term in this equation is divided by 5, it becomes w + q = l; SUFFICIENT.

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

Correct Answer: B

Explanation:

Geometry Circles

• (1) The maximum distance between two points that lie on a circle is equal to the diameter, or 2 times the radius. Since the radius of circle C is 2, the diameter in this case is 4. It cannot be assumed, however, that X and Yare points on the diameter; X can lie anywhere within the circle. When the distance between X and Y is 3, it is still possible either that Y is within the circle or that Y is outside the circle; NOT sufficient.
• (2) If the length of the line segment OY is 1.5 and the circle has a radius of 2, then the distance from the center 0 to point Y is less than the radius, and point Y must therefore lie within the circle; SUFFICIENT.

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