Data Sufficiency

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
(1) The average (arithmetic mean) salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.
(2) The average (arithmetic mean) salary of the managers on the task force is $15000 greater than the average salary of all employees on the task force.


Can anyone give me an explanation of the answer? (C)

This problem too:

The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meters thick?
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of square slab that is 2 meters long and 0.1 meter thick

(answer is D)

and this problem:

If n and t are positive integers, what is the greatest prime factor of the product nt?
(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

(answer is B)

nz11 wrote:Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
(1) The average (arithmetic mean) salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.
(2) The average (arithmetic mean) salary of the DIRECTORS on the task force is $15000 greater than the average salary of all employees on the task force.


Can anyone give me an explanation of the answer? (C)

this one uses Weighted average concept.

Nm * Am + Nd * Ad =( Nm +Nd) *T

where Am, Ad, T denotes respective salaries & Nm ,Nd denote their numbers.

frm st 1 wkt; Am = T-5000 & frm st 2 we know that; Ad= T+15000

Use the above 2 values in the main equation and solve for Nd/Nm & then find Nd/(Nm+Nd) which the prompt asks for.

cost (C) = k (thickness * length^2) or C = k.T.L^2
where thickness = T and length = L and K = constant
we need to find the cost of sq slab 3 mts long and 0.1 mts thick so C = k.(0.1) * (3^2)
or C = 0.9k

stat 1: 0.8k - 160 = 0.4k or k = 400
hence sufficient to find C

stat 2: 0.9k - 200 = 0.5k or k =400
again sufficient to find C

thus answer = D each statement alone sufficient to find the solution

nz11 wrote:This problem too:

The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meters thick?
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of square slab that is 2 meters long and 0.1 meter thick

(answer is D)

given n>0, t>0 to find greatest prime factor of nt

stat 1: gcf of n and t = 5 states that 5 is the largest number that divides both numbers n and t completely. it doesn't comment on the greatest prime factor of each number n and t which can vary with different numbers. hence not sufficient

stat 2: LCM of n and t = 105. prime factors of 105 = 3*5*7
largest prime factor of lcm of 2 nos = largest prime factor of product of 2 numbers n and t (ie n*t)
hence largest prime factor of nt = 7
sufficient

statement B alone is sufficient.

nz11 wrote:and this problem:

If n and t are positive integers, what is the greatest prime factor of the product nt?
(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

(answer is B)