10 questions. Try each one, then open the answer to check yourself and read the explanation.
When the price of egg was raised by ₦2 an egg. The number of eggs which can be bought for ₦120 is reduced by 5. Find present price of an egg
Answer: C (₦8)
If the old price is x, 120/x − 120/(x + 2) = 5, which gives x2 + 2x − 48 = 0, so x = 6 and the present price is ₦8.
Find the number of terms in an arithmetic given that the first and last terms are a and 37a respectively and that its common difference is 4a
Answer: B (10)
37a = a + (n − 1)4a gives 36a = 4a(n − 1), so n − 1 = 9 and n = 10.
A certain deck of cards contains r cards. After the cards are distributed evenly among 5 people, 8 cards are left over. In terms of r and s, how many cards did each person received?
Answer: C ((r − 8)/s)
r − 8 cards are shared equally among s people, so each gets (r − 8)/s.
Ade would be x years old y years to this time. How old was he z years ago?
Answer: D (x − y − z)
He is now x − y years old, so z years ago he was x − y − z.
The sum of the digits of a two-digit number is 15. If the digits are interchange the number is increased by 9. Find the number
Answer: A (78)
Swapping digits adds 9, so the units digit is 1 more than the tens digit: tens + units = 15 gives 7 and 8, so 78.
A three-digit number is such that the sum of its digit is 12. The middle is half the sum of the other two and the last digit is three times the first one. Find the number
Answer: B (246)
Let the first digit be x: the last is 3x and the middle is 2x, so 6x = 12, x = 2, giving 246.
The sum of the ages of a man and his son is 67 years. Six years ago the man's age exceeded 5 times the age of his son by 1. Find their present ages.
Answer: A (Man = 52 years son = 15 years)
x + y = 67 and x − 6 = 5(y − 6) + 1 give x − 5y = −23; subtracting, 6y = 90, so y = 15 and x = 52.
Figure above shows the lengths of the sides of an equilateral triangles in centimeters. Find the values of x and y.
Answer: B (x = 5, y = 2)
All sides are equal: 2x − 1 = x + 2y and x + 2y = 3y + 3 give x − 2y = 1 and x − y = 3, so y = 2 and x = 5.
In one month, a man spent ₦650 on newspapers and ₦240 on soap. The next month, he reduced his newspaper spending by 40%. If the ratio of the amount spent on soap in the second month to that of the first month is 5:3, what is the difference in the amount spent on both items in the two months.
Answer: B (₦10)
Second month: newspapers 60% of 650 = ₦390 and soap 5/3 × 240 = ₦400, so the two items differ by ₦10.
The average of the three children in a family is 9 years. If the average age of their parent is 39 years, what is the average age of the whole family?
Answer: D (21 years.)
Children total 27 years and parents 78 years, so the 5 members average 105 ÷ 5 = 21 years.