SAT (Stage-1) Mock Test

Result

SAT (Stage-1) Mock Test - 44

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Weekly Quiz Competition

Question 1
1 / -0

A box of marbles and a book cost £6.2. If the book costs £3.5 less than 1 box of marbles, then find the total cost of 4 books and 2 boxes of marbles.

A
£7.9

B
£10.5

C
£13.6

D
£15.1

Solution

Let the cost of 1 book be £x.
And cost of 1 box of marbles = £y
x + y = 6.2 .…(1)
x = y - 3.5
or x - y = -3.5 ….(2)
Adding equations (1) and (2):
x + x = 6.2 + (-3.5)
2x = 6.2 - 3.5
2x = 2.7
x = 2.7/2
x = 1.35
Put x = 1.35 in equation (1):
1.35 + y = 6.2
y = 6.2 - 1.35
y = 4.85
Cost of 4 books and 2 boxes = 4x + 2y
= 4 × 1.35 + 2 × 4.85
= 5.4 + 9.7 = £15.1
Question 2
1 / -0

Which digit is at the 99^th decimal place in the decimal value of 5/7 ?

A
0

B
1

C
4

D
5

Solution

5/7 = 0.71428571428571...
Period is 714285 and periodicity is 6. 99 = 6(16) + 3. So, at the 99^thdecimal place, the digit is 4.
Question 3
1 / -0

If a and b are the roots of x² + px - q = 0, and g and d are the roots of x² + px + r = 0, then the value of (a - g)(a - d) is

A
p + r

B
q + r

C
p + q + r

D
None of these

Solution

a + b = g + d = -p
ab = -q, and
gd = r
Value of (a - g)(a - d) = a² - ga + gd - ad = a²- (g + d)a + gd = a² - (a + b)a + gd = gd - ab = r + q