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Algebra Level 1 Test 1

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Question 1
P is the prime number, where P is ≥5 , therefore ( P-1 )( P+1 ) is always divisible by
A
12
B
24
C
6
D
48
Question 1 Explanation: 
Answer is 24 The easiest approach is to consider the value of P as 5, 7, 11, 13. As prime numbers are of the form, is either 6k+1 or 6k-1 hence the number is always divisible by 24
Question 2
( 525 ) 35 =5x . Find the Value of X
A
60
B
875
C
3525
D
2535
Question 2 Explanation: 
As we know   (am)= amn Hence Value of x = 25*35 = 875
Question 3
( P+Q )2 = 196 , PQ = 48 Find the value of P2+ Q2
A
100
B
50
C
148
D
52
Question 3 Explanation: 
(p + q)2 = p2 + 2pq + q2 Hence P2+ Q2 = 196- 2*48 = 100
Question 4
( P+Q )2 = 676 , PQ = 160 Find the value of P2- Q2
A
376
B
96
C
156
D
36
Question 4 Explanation: 
(P + Q)2 = P2 + 2PQ + Q2 (P - Q)2 = P2 – 2PQ + Q2 P+Q = 26 ; P-Q= 6 P= 16 Q= 10 hence P2- Q2 = 256- 100 = 156
Question 5
324 / 32  =3x . Find the Value of X
A
12
B
22
C
24
D
√24
Question 5 Explanation: 
As we know   am/ a= am-n Hence the answer should be = 24-2 = 22
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