Direction: The data shows the total number of male and female employees in…

2020

Direction: The data shows the total number of male and female employees in three companies at a seminar. Read the data carefully and answer the question.

In the annual seminar of three companies A, B and C, some male and female employees represent their companies. The average number of female employees who represent A and B is 420. The total number of male employees in A and B is 1620. The number of female employees is two-thirds and two-fifths of the male employees in A and B respectively. The total number of female employees who represent C is 25% more than the total female employees who represent A, and the total number of male employees who represent C is 33⅓% more than the total female employees who represent B.

The total number of employees who represent A is what percent more than the total number of male employees who represent B?

  1. A.

    33⅓ %

  2. B.

    30⅓ %

  3. C.

    27⅓ %

  4. D.

    29⅓ %

  5. E.

    39⅓ %

Show answer & explanation

Correct answer: A

Concept

In a data-interpretation set the unknown counts are linked by ratio and total relations. The method is: turn each verbal relation into one equation, solve the linked equations for the base quantities, then read off whatever the question asks. The 'percent more' of P over Q is (P − Q) ÷ Q × 100.

Application

  1. Let the male counts be MA and MB. Females are given as fractions of males, so FA = (2/3)·MA and FB = (2/5)·MB.

  2. Total males in A and B: MA + MB = 1620.

  3. Average of females in A and B is 420, so FA + FB = 2 × 420 = 840.

  4. Substitute the fractions: (2/3)·MA + (2/5)·MB = 840. Using MB = 1620 − MA, expand to (2/3)·MA + 648 − (2/5)·MA = 840.

  5. Combine like terms: (2/3 − 2/5)·MA = 192, i.e. (4/15)·MA = 192, so MA = 720 and MB = 900.

  6. Then FA = (2/3)·720 = 480 and FB = (2/5)·900 = 360.

  7. Total employees in A = MA + FA = 720 + 480 = 1200. Male employees in B = 900.

  8. Percent more = (1200 − 900) ÷ 900 × 100 = 300/900 × 100 = 33⅓%.

Cross-check

Independent check: 1200 = 900 × 4/3, and 4/3 = 1 + 1/3, so A's total is exactly one-third above B's male count — a clean 33⅓%, confirming the result. The values FA + FB = 840 and MA + MB = 1620 also satisfy the original totals.

Explore the full course: Niacl Ao It Specialist