Data Sufficiency MCQ Set 4

Correct Answer: B

Explanation:

Arithmetic Statistics

The formula for calculating the arithmetic mean, or the average, is as follows: Average = sum of v values / v

• (1) These data will produce an average of 2160/30 = 72° for last April in City X. However, there is no information regarding the median for comparison; NOT sufficient.
• (2) The median is the middle temperature of the data. As such, 50 percent of the daily high temperatures will be at or above the median, and 50 percent will be at or below the median. If 60 percent of the daily high temperatures were less than the average daily high temperature, then the average of the daily highs must be greater than the median; SUFFICIENT.

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

Correct Answer: A

Explanation:

Arithmetic Properties of numbers

• (1) If (√M ) is an integer and n is a positive integer, then (√M )ⁿ is an integer because an integer raised to a positive integer is an integer; SUFFICIENT.
• (2) The information that (√n ) is an integer is not helpful in answering the question. For example, if m = 2 and n = 9, -√9 = 3, which is an integer, but (√2⁹ ) = (l6 √2), which is not an integer. But if m = 4and n=9, then √9 = 3, which is an integer, and (√4 )⁹ = 2⁹ = 512 is an integer; NOT sufficient.

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

Correct Answer: D

Explanation:

Algebra Sets and functions

Because it is given that 6 is the greatest number of individuals who can have birthdays in any particular month, these 66 people could be evenly distributed across 11 of the 12 months of the year. That is to say, it could be possible for the distribution to be 11 X 6 = 66, and thus any given month, such as January,would not have a person with a birthday. Assume that January has no people with birthdays, and see if this assumption is disproved.

• (1) The information that more people have February birthdays than March birthdays indicates that the distribution is not even. Therefore, March is underrepresented and must thus have fewer than 6 birthdays. Since no month can have more than 6 people with birthdays, and every month but January already has as many people with birthdays as it can have, January has to have at least 1 person with a birthday; SUFFICIENT.
• (2) Again, March is underrepresented with only 5 birthdays, and none of the other months can have more than 6 birthdays. Therefore, the extra birthday (from March) must occur in January; SUFFICIENT.

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

Correct Answer: E

Explanation:

Arithmetic Statistics

• (1) Since all 10 employees did not receive the same 15 percent increase, it cannot be assumed that the mean this year is 15 percent higher than last year. It remains unknown whether these 8 salaries were the top 8 salaries, the bottom 8 salaries, or somewhere in-between. Without this type of information from last year, the mean for this year cannot be determined; NOT sufficient.
• (2) If 2 salaries remained the same as last year, then 8 salaries changed. Without further information about the changes, the mean for this year cannot be determined; NOT sufficient.

Even taking (1) and (2) together, it remains impossible to tell the mean salary for this year without additional data.

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

Correct Answer: D

Explanation:

Algebra Sets and functions

Let x represent the fiction books that are written in Spanish. A table could be set up like the one below, filling in the information that is known or able to be known:

• (1) If a; represents the fiction books written in Spanish, then x+6 can now be used to represent the fiction books that are not written in Spanish. From the table above, it can be seen then that x + x + 6 = 24, or 2x = 18. Therefore, x, or the number of fiction books written in Spanish, is 9; SUFFICIENT.
• (2) If x represents the fiction books written in Spanish, then x+ 5 can now be used to represent the nonfiction books written in Spanish. From the table, it can be said that x + x + 5 = 23, or 2x = 18. Therefore, x, or the number of fiction books written in Spanish, is 9; SUFFICIENT.

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

Correct Answer: C

Explanation:

Geometry Rectangles; Perimeter; Area

The perimeter of a rectangle is equal to 2 times the rectangle's length plus 2 times the rectangle's width, or p = 21 + 2w. The diagonals of a rectangle are equal. In a rectangle, because a diagonal forms a right triangle, the length of a diagonal is equal to the square root of the length squared plus the width squared, or d = √ t² + w ².

• (1) If a diagonal = 10, then 10 = √ t² + w ², or, by squaring both sides, 100 = I² + w². Without knowing the value or the relationship between the other two sides of the right triangle, it is impossible to solve for / or w, and thus for the perimeter of the rectangle; NOT sufficient.
• (2) If the area of the rectangle is 48, then it can be stated that I w = 48. However, without further information, the perimeter cannot be determined. For example, / could be 6 and w could be 8, and the perimeter would then be 12 + 16 = 28. However, it could also be that / is 4 and w is 12,and in that case the perimeter would be 8+ 24 = 32; NOT sufficient.

Using (1) and (2) together, it is possible to solve this problem. Since from (2)I w= 48, then w = 48/I. Substituting this into 100 =I² +w² from (1) the equation can be solved as follows: 100 = I² + (48/I)² + substitution
100 I² = I⁴ + 2,304 multiply both sides by I²
l⁴ - 100 I² + 2,304 = 0 move all terms to one side
(l² - 64)(I² - 36) =0 factor like a quadratic
I² =64,I² = 36 solve for I²
Since I is a length, it must be positive, so I is 48 either 8 or 6. When I = 8, w = -5- = 6, and when I = 6, w = -48/6 = 8, both of which give the same perimeter.

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