SAT (Stage-1) Mock Test

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SAT (Stage-1) Mock Test - 90

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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 99th 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

A
62

B
52

C
48

D
64

Solution
Question 4
1 / -0

If a²/bc + b²/ca + c²/ab = 3 and a ≠ b, then a + b + c = ?

A
3abc

B
3

C
abc

D
0

Solution

Hence, a³ + b³ + c³ = 3abc
a³ + b³ + c³ - 3abc = 0
Hence, (a + b + c)(a² + b² + c² - ab - bc - ca) = 0
∴ a + b + c = 0
Question 5
1 / -0

What number should be subtracted from 2x² - 7x - 12 so that the resulting polynomial has a factor 2x + 3?

A
-3

B
3

C
0

D
- √3

Solution
Question 6
1 / -0

A bag contains 6 white and 9 black balls. If three balls are drawn at random, then find the probability that all of them are black.

A
27/125

B
12/65

C
74/455

D
1/5

Solution

Total number of outcomes = ¹⁵C₃
Number of favourable outcomes = ⁹C₃
Question 7
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
Question 8
1 / -0

In a parallelogram ABCD, ∠A : ∠B = 1 : 2. Find the value of ∠C.

A
120°

B
50°

C
60°

D
30°

Solution

∠A : ∠B = 1 : 2

Let ∠A = x and ∠B = 2x
Also, ∠A + ∠B = 180° [Adjacent angles of a parallelogram are supplementary.]
⇒ x + 2x = 180°
⇒ 3x = 180°
⇒ x = 180°/3 = 60°
And ∠A = ∠C [∵Opposite angles of a parallelogram are equal.]
⇒ ∠C = 60°
Alternate method: ∠A = ∠C and ∠B = ∠D [∵ Opposite angles of a parallelogram are equal.]
And ∠A : ∠B = 1 : 2
⇒ ∠A = x and ∠B = 2x
Then, ∠A + ∠B + ∠C + ∠D = 360° [Angle sum property of a quadrilateral]
⇒ x + 2x + x + 2x = 360°
⇒ 6x = 360° ⇒ x = 60°
⇒ ∠A = ∠C = 60°
Question 9
1 / -0

Mean of seven numbers is 52 and six of those numbers are 17, 19, 15, 8, 5 and 12. Find the missing number.

A
74

B
106

C
288

D
None of these

Solution

Let the 7^th number be x.

52 × 7 = 17 + 19 + 15 + 8 + 5 + 12 + x

364 = 76 + x

Or, x = 364 - 76

x = 288
Question 10
1 / -0

A tap drips at an average rate of 2 drops every 3 seconds. It takes 2080 such drops of water collected to completely fill a vessel of hemispherical shape (radius 8.3 cm). How many times can the vessel be filled in this manner over 13 hours?

A
10

B
11

C
13

D
15

Solution

Average rate of dripping = 2/3 drops/sec
Total number of drops in the completely filled vessel = 2080
Then, time taken by the tap to drip 2080 drops = 3/2× 2080 = 3120 sec
∴Number of times vessel will be filled over 13 hours = 13×3600 / 3120 = 15
Question 11
1 / -0

In the figure below, the area of triangular region PQR is 36 sq. units. What is the area of triangular region SQR?

A
12 sq. units

B
16 sq. units

C
24 sq. units

D
30 sq. units

Solution

In triangle PQS, PQ² + PS² = QS²
4² + PS² = 5²
PS² = 9 units
PS = 3 units
Area of triangle PQS = 1/2 × 4 × 3 = 6 sq. units
Now, area of triangle SQR = ar(PQR) - ar(PQS)
= 36 - 6 = 30 sq. units
Question 12
1 / -0

A
9 : 4

B
14 : 9

C
1 : 2

D
1 : 12

Solution
Question 13
1 / -0

The angle of elevation of a 15 m high tower is 60° from the bottom of an electric pole. The angle of elevation of the tower from the top of the electric pole is 30°. Find out the height of the electric pole.

A
5 m

B
8 m

C
10 m

D
12 m

Solution

Consider the diagram:

Let AB and CD be the heights of the tower and the electric pole, respectively.
Then, ∠ACB = 60°, ∠EDB = 30° and AB = 15 m
If CD = h,
then BE = (AB – AE) = (AB – CD) = (15 – h)
Question 14
1 / -0

Standing at a radar base, a person observes an unidentified object at a height of 3000 m flying towards the radar station at an angle of elevation of 30°. After a minute, the person again observes that the flying object is at an angle of elevation of 60°, having the same height. What is the speed of the object?

A
54 m/s

B
55 m/s

C
56.80 m/s

D
57.73 m/s

Solution

Distance travelled in 1 minute = ST = QR = PR - PQ
Question 15
1 / -0

If sin²θ + 3 cosθ - 2 = 0, then cos³θ + sec³θ is equal to

A
18

B
9

C
4

D
1/4

Solution

Given sin²θ + 3 cosθ - 2 = 0
⇒ cos²θ - 3 cosθ + 1 = 0
⇒ cos²θ + 1 = 3 cosθ
dividing by cosΘ on both sides. so,

from (i)
⇒ cos³θ + sec³θ + 3(3) = 27
⇒ cos³θ + sec³θ = 18