1999 - JAMB Mathematics Past Questions and Answers - page 1
1
A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
A
25
B
19
C
18
D
17
correct option: a
Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
Users' Answers & Commentsn{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.
2
If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A
\(\frac{1}{2}\)X
B
X-\(\frac{1}{4}\)
C
X-\(\frac{1}{3}\)
D
X-\(\frac{1}{2}\)
correct option: c
\(log_810\) = X = \(log_8{2 x 5}\)
\(log_82\) + \(log_85\) = X
Base 8 can be written as \(2^3\)
\(log_82 = y\)
therefore \(2 = 8^y\)
\(y = \frac{1}{3}\)
\(\frac{1}{3} = log_82\)
taking \(\frac{1}{3}\) to the other side of the original equation
\(log_85 = X-\frac{1}{3}\)
explanation courtesy of Oluteyu and Ifechuks
Users' Answers & Comments\(log_82\) + \(log_85\) = X
Base 8 can be written as \(2^3\)
\(log_82 = y\)
therefore \(2 = 8^y\)
\(y = \frac{1}{3}\)
\(\frac{1}{3} = log_82\)
taking \(\frac{1}{3}\) to the other side of the original equation
\(log_85 = X-\frac{1}{3}\)
explanation courtesy of Oluteyu and Ifechuks
3
Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\)
A
3√2+4
B
3√2-4
C
3-2√2
D
4+2√2
correct option: a
Start your solution by cross-multiplying, then collect like terms and factorize accordingly to get the unknown.
Users' Answers & Comments4
If \(\frac{(a^2 b^{-3}c)^{\frac{3}{4}}}{a^{-1}b^{4}c^{5}}=a^{p} b^{q} c^{r}\) What is the value of p+2q?
A
(5/2)
B
-(5/4)
C
-(25/4)
D
-10
correct option: d
Hint: apply basic mathematics rules beginning from BODMAS to algebra, and follow solution carefully to arrive at p =(5/2), q = -(25/4) and r = -(9/2).
Then p+2q will give you \(\frac{5}{2}+2\left(\frac{-25}{4}\right)= -10\)
Users' Answers & CommentsThen p+2q will give you \(\frac{5}{2}+2\left(\frac{-25}{4}\right)= -10\)
5
If {(a2b-3c)3/4/a-1b4c5} = apbqcr; what is the value of p+2q?
A
(5/2)
B
-(5/4)
C
-(25/4)
D
-10
correct option: d
Hint: Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.
Then substitute the values of p and q into p+2q to get -10.
Users' Answers & CommentsThen substitute the values of p and q into p+2q to get -10.
6
A trader bought 100 oranges at 5 for N1.20, 20 oranges got spoilt and the remaining were sold at 4 for N1.50. Find the percentage gain or loss.
A
30% gain
B
25% gain
C
30% loss
D
25% loss
correct option: b
Cost price (cp) = (100/5) x N1.20 =N24.00
Selling price (sp) = 100-20 = 80
(80/4) x N1.50 = N30.00
Gain = SP-CP = N30.00-N24.00 = N6.00
Gain% = (gain/CP) x 100 = 25%
Users' Answers & CommentsSelling price (sp) = 100-20 = 80
(80/4) x N1.50 = N30.00
Gain = SP-CP = N30.00-N24.00 = N6.00
Gain% = (gain/CP) x 100 = 25%
7
What is the answer when 24346 is divided by 426?
A
236
B
356
C
526
D
556
correct option: b
Hint: Two methods can be used;
1. Direct division (if you know division in number bases)
2. Convert both sides to base 10, divide and convert your answer back to base 6. Your answer should be 356
Users' Answers & Comments1. Direct division (if you know division in number bases)
2. Convert both sides to base 10, divide and convert your answer back to base 6. Your answer should be 356
8
If 29 x (3Y)9 = 35 x (3Y)5, find the value of Y.
A
4
B
3
C
2
D
1
correct option: d
The correct answer is 1.
PROVE==> (2x90) (3x90 + Yx91) = (3x50)(3x50 + Yx51).
You multiply to get 2(3+9Y)=3(3+5Y).
You further multiply to get 6+18Y=9+15Y. ==>
Collect like terms 18Y-15Y=9-6.
3Y/3=3/3.
Y=1
Explanation Credit:
Users' Answers & CommentsPROVE==> (2x90) (3x90 + Yx91) = (3x50)(3x50 + Yx51).
You multiply to get 2(3+9Y)=3(3+5Y).
You further multiply to get 6+18Y=9+15Y. ==>
Collect like terms 18Y-15Y=9-6.
3Y/3=3/3.
Y=1
Explanation Credit:
9
Simplify \(\sqrt{\frac{(0.0023*750)}{(0.00345*1.25)}}\)
A
15
B
20
C
40
D
75
correct option: b
Multiply appropriately to remove decimals on both numerator and denominators. Such that you have \(\sqrt{\frac{(2300x750)}{(345x125)}}
Dividing, => \sqrt400 = 20\).
Users' Answers & CommentsDividing, => \sqrt400 = 20\).
10
If \(m*n = (\frac{m}{n} - \frac{n}{m}\)) for m, n belong to R, evaluate -3*4
A
\(\frac{-25}{12}\)
B
\(\frac{-7}{12}\)
C
\(\frac{7}{12}\)
D
\(\frac{25}{12}\)
correct option: c
\(m*n = \frac{m}{n}-\frac{n}{m}
= \frac{-3}{4} - \frac{4}{-3}
= \frac{-3}{4} + \frac{4}{3}
= \frac{(-9+16)}{12}
= \frac{7}{12}\)
Users' Answers & Comments= \frac{-3}{4} - \frac{4}{-3}
= \frac{-3}{4} + \frac{4}{3}
= \frac{(-9+16)}{12}
= \frac{7}{12}\)