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Algebra Level 2 Test 9

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Question 1
A person brought 5 tickets from a station P to a station Q and 10 tickets from the station P to a station R. He paid Rs. 350. If the sum of a ticket from P to Q and from P to R is Rs. 42, then what is the fare from P to Q
A
12
B
14
C
16
D
18
Question 1 Explanation: 
Let the fares of both the stations i.e. from P to Q and from P to R  be = a and b
So from the question we can say that
5a + 10b = 350………………………..1
And a + b = 42…………………………2
From equation 1 and 2
5a =70
a = 70/5 = 14
Question 2
In a class room there are certain numbers of benches. If 6 students are made to sit on a bench then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left. What is the total number of students in the class?
A
30
B
42
C
72
D
cannot determine
Question 2 Explanation: 
Let the number of boys in the class = p
Let the number of girls in the class = q
pq + qp = 1600
pq = 800 from the question we are given by that
p +q = 60
by solving the equations
p  = 40 or 20
Since there are two values of p, we cannot determine the answer.
Question 3
For which of the following value of p the 2p2 +6p <3 is satisfied?
A
p < -3 and p > 1/2
B
-3 < p < 1/2
C
-1/2

D
½

Question 3 Explanation: 
2p2 +6p <3 = 2p2 +6p – 3 < 0
= 2p2 +6p –p-3 <0
= 2p(p +3) – 1(p +3) < 0
= (2p -1) (p +3) < 0
This is possible only when either (2p -1) > 0 and (p+3) <0 or (2p -1) < 0 and (p+3) >0
This means there will be two cases
(2p -1) > 0 = x <1/2 and (p+3) <0 = p > -3 which is possible
So option (b) satisfies the condition.
Question 4
In a certain party, there was a bowl of rice for every two guests, a bowl of broth for every three of them and a bowl of meat for every four of them. If in all there were 65 bowl of food, then how many  guests were in the party
A
65
B
24
C
60
D
48
Question 4 Explanation: 
Let the number of rice bowl , broth bowl and meat bowl = p ,q, r respectively
Therefore p + q+ r = 65
It is given that 2p = 3y = 4z
From these equations, we get the value of p = 30,q= 20 and r = 15
Therefore the total number of guests are = 60
Question 5
If the value of p11 = q0 and  p = 2q , then what will be the value of q?
A
1/2
B
1
C
-1
D
-2
Question 5 Explanation: 
Given that p11 = q0
But we know that any number raised to the power 0 is one so q0 = 1
That means p11 = 1
P = 1
And now we are given by that
p = 2q
q = ½ option number (a)
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