Numbers(Study by Topics Senior Class) : GATE Academy

Welcome to your Numbers(Senior Class Math Study by Topics)

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PHONE NUMBER

1. Solve for x
if
(5x)₇ = 37₁₀

2. Two brothers Kameel and Kafeel owned a business in which the ratio of shares was 3 : 2 respectively.
Kafeel later sold ½ of his share to Kameel for £12,000.
The value of the business was

£60,000

£48,000

£84,000

£24,000

3. If 101₂ x P₂= 11110₂,
find the value of P

101

110

4. If R = {2, 4, 6, 7} and S = {1, 2, 4, 8}
find R∪S

{1, 2, 4, 6, 7, 8}

{2,7}

{4}

{}

5. A bag contains white, blue and red ping pong balls in the ratio 8 : 3: 2.
There are 10 red balls.
If 10 white and 10 blue balls are removed from the bag,
the new ratio is

7 : 1 : 2

7 : 2 : 1

6 : 1 : 1

6 : 1 : 2

6. Two friends Tyson and Kourtney went out to lunch at a restaurant.
If Tyson contributed 40% of the cost and Kourtney contributed the balance,
which is $150, the cost of the lunch was

$300

$260

$375

$250

7. The ratio of the price of a tin of milk to that of a packet of sugar is m : p.
If the price of milk now goes up by 25% while that of sugar goes up by 15%,
the new ratio of the prices is

25m : 23p

5p : 3m

23m : 25p

3p : 5m

8. A sum of N420 is shared among three children in the ratio 6 : 7 : 8.
The largest share is

N180

N160

N120

N140

9. A sum of money invested at a simple interest rate R increases to 5/3 times the original sum after 5 years.
The value of R is

10.5%

9.0%

6.0%

13.3%

10. A trader bought 132 oranges at C30 each, and sold them at C42 each,
where C is the currency reckoned in base 4,
the profit is

C3210 base 4

C2310 base 4

C2210 base 4

C231 base 4

11. A school has 43 students in class 3A and 47 students in 3B.
The average score in a test is 55 for class 3A and 60 for class 3B.
The average score for both classes, correct to one decimal place, is

57.5

57.6

58.1

57.8

12. If X= {1, 2, 3, 4} and
Y = {3, 5, 6},
the elements of (X ∩ Y) ∪ X are

{1,2,4}

{3}

{1,2,3,4}

{3,5,6}

13. In a certain class, 37 students take at least one of Chemistry, Economics and History.
8 students take Chemistry, 19 take Economics and 25 take History.
12 students take Economics and History but nobody takes Chemistry and Economics .
How many students take both Chemistry and History?

14. The universal set U contains all integers. Subsets of U are defined as
P = {x : x ≤ 3}
Q = {x : -5 < x < 12}
R = {x : -2 ≤ x < 5}
P ∩ Q = ?

{-4, -3, -2, -1, 0, 1, 2, 3}

an infinite set

{1, 2, 3}

{0, 1, 2, 3}

15. Given that P = {1, 2, 3, 4};
Q ={5, 6, 7, 8} and
R = {1, 2, 3, 2, 4, 2},
it follows that
I. P = R
II. n(R) = 6
III. n(P ∪R) = 4
Which of the statements above is (are) true?

II only

I only

I and III only

III only

16. If the Universal set U = {x: x is a natural number and 1 ≤ x ≤ 9}
P = {x: 1 ≤ x ≤4}
Q = {2, 4, 6, 8}

Find (P ∪ Q)'

{5, 7, 9}

{6, 4, 9}

{2, 3}

{9}

17. P and Q are two sets such n(P ∪ Q) is 50, n(P) is 40 and n(Q) is 18.
What is n(P ∩ Q)

108

18. Zara deposited £1500.00 in her bank account.
At the end of five years the simple interest on the account amounted to £550.00. The rate per annum of interest was

7.33%

4.5%

19. After getting a pay rise of 20%, a man's new annual salary is N21,600.
His salary before the pay rise was

N17,280

N17,700

N18,000

N16,680

20. A number of chocolates were shared out among three children Kafeel, Tara and Kameel in the ratio 2:3:4 respectively.

If Kameel got 8, how many sweets were shared out?

21. If (1Y14)₅ = 184₁₀,
the value of Y is

22. A plumber's daily wage is £80 for the first 10 days and £100 for the next 9 days. Find the daily wage for the remaining 6 working days of the month, if his average daily wage for the month is £90.80

£95

£105

£110

£92.50

23. The lowest common multiple of the prime numbers between 1 and 10 is

210

105

24. If X = {prime factors of 84} and
Y = {prime factors of 315},
the elements of X∪Y and X∩Y are, respectively

{3, 4, 5, 7,} and {5, 7}

{3, 4, 5, 7, 9} and {3, 7}

{2, 3, 5, 7} and {3, 7}

{4, 3, 2, 5} and {1, 3}

25. A sum of £50,000 was invested by two partners in a project which yielded £90,000. If the profit was shared in the ratio 3 : 5, the difference between the amounts received by the partners is

£25,000

£40,000

£15,000

£10,000

26 out of 25

Numbers(Study by Topics Senior Class)

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