Algebra Level 1 Test 2

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Algebra Level 1 Test 2

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Question 1

If x + 1/x = 13, what is the value of x² + 1/x²?

A	169
B	167
C	143
D	26

Question 1 Explanation:

x + 1/x = 13
(Squaring both sides)
x² + 1/x² + 2.x.1/x = 169.
x² + 1/x² = 169 – 2 = 167.

Question 2

Find the value of X & Y in 3X + 4Y = 25 ,4X – 2Y = 4

A	X = 4 Y = 3
B	X = 3 Y = 4
C	X = 5 Y = 3
D	X = 3 Y = 3

Question 2 Explanation:

Multiply the second equation with 2 and then add
both the equations, we get X= 3 and Y= 4

Question 3

If product of the two numbers is 24, find the Maximum value of the sum of the numbers ?

A	25
B	10
C	14
D	11

Question 3 Explanation:

The sum of the number will be maximum when the
difference of the number is maximum :
Hence axb= 24 so possible solution can be 1*24 = 24 (hence a=1 b =24 )
Maximum value of the sum = 1+24= 25

Question 4

If (a + b) = 36 and ab = 323, find (a – b)

A	6
B	2
C	1
D	7

Question 4 Explanation:

As a x b = 323, so possible pairs are 17 x 19 , 323 x 1
So only possible pair for a+b= 36 is when a=17 b=19
Thus, the difference is option b

Question 5

If (a + b) = 70 and ab = 1221, find (a – b)

A	6
B	2
C	4
D	7

Question 5 Explanation:

As a x b = 1221 = so possible pairs are 37 x 33 ,
111 x 11 , 1221 x 1
So only possible pair for a+b= 70 is when a=37 b=33
Thus, the difference is option 3

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