PSAT SAMPLE QUESTIONS ONLINE

Question 1 :

 √100 √64  =  

(A)  8  (B)  10  (C)  18  (D)  80  (E)  164

Solution :

 √100 √64  =   √(10 ⋅ 10) √(8 ⋅ 8)

  =  10 (8)

  =  80

Hence the answer is 80.

Question 2 :

7.2 aliens  =  1 monster

1 monster  =  15.5 oranges

Using the conversion above, how many oranges are equal to 1 alien ?

(A)  0.46  (B)  1.95  (C)  2.15  (D)  22.7  (E)  111.6

Solution :

1 monster  =  7.2 aliens   ----(1)

1 monster  =  15.5 oranges  ----(2)

(1)  =  (2)

7.2 aliens  =  15.5 oranges

1 alien  =  15.5/7.2

=  2.15

Hence the answer is 2.15

Question 3 :

What is the greatest common factor of 147 and 198 ?

(A)  2  (B)  3  (C)  7  (D)  14  (E)  49

Solution :

There is no common divisor for 49 and 66. Hence the greatest common factor is 3.

Question 4 :

If x  =  7 and y  =  0, what is the value of 11x / (x - y) ?

(A)  0  (B)  7  (C)  10  (D)  11  (E)  77

Solution :

11x / (x - y)  =  11(7) / (7 - 0)  ==>  77/7  ==>  11

Hence the answer is 11.

Question 5 :

Heiga has 4 dogs, 3 cats and 2 birds. If she closes her eyes and picks one animal. What is the probability that it does not have 4 legs ?

(A)  3u/7  (B)  2/7  (C)  7/9  (D)  2/9  (E)  4/7

Solution :

Sample space  =  Total number of animals 

  =  3 + 4 + 2

n(S)  =  9

Dogs and cats have 4 legs, and birds has 2 legs.

Number of animals do not have 4 legs  =  2 

n(A)  =  2

P(A)  =  n(A) / n(S)

P(A)  =  2/9

Hence the required probability is 2/9.

Question 6 :

If y = x²⋅x^x, what is y when x = 2 ?

(A)  16  (B)  8  (C)  4  (D)  32  (E)  0

Solution :

y  =  x²⋅x^x

y  =  x^{(2 + x)}

y  =  2^{(2 + 2)}

y  =  2⁴

y  =  16

Hence the answer is 16.

Question 7 :

Train A, travelling at 200 mph, leaves station A at 1 P.M train B travelling at 300 mph, leaves station B at 3 P.M. Both stations are directly across each other and X miles away. If the trains meet at 4 P.M, What is X ?

(A)  500 ml  (B)  900 ml  (C)  700 ml 

(D)  600 ml  (E)  400 ml

Solution :

From the given information, we know that both trains meet at 4 P.M.

Train A has traveled for 3 hours at the speed of 200 mph

Train B has traveled for 1 hour at the speed of 300 mph

Distance covered by both trains together 

=  600 miles + 300 miles

  =  900 miles

Hence both trains will meet each other apart 900 miles.

Question 8 :

Bernard is now y years old. Luis is 8 years older than Bernard. In terms of y, how old was Luis 5 years ago?

(A)  8y  (B)  8y - 5  (C)  y + 3  (D)  y + 13  (E)  y - 5

Solution :

Age of Bernard  =  y

Age of Luis  =  y + 8

5 years ago Luis age  =  y + 8 - 5

  =  y + 3

Question 9 :

In a figure above, ABC, DBE, EFG and CFH are straight line segments. What is the value of x ?

(A)  25  (B)  45  (C)  65  (D)  70  (E)  75

Solution : 

In a quadrilateral BEFC,

<GFH  =  <EFC  =  65 (Vertically opposite angles)

<CBE + <BEF + <EFC + <FCB  =  360

<CBE + 110 + <EFC + 110  =  360

<CBE + 220 + 65  =  360

<CBE  =  360 - 285

<CBE  =  75

x =  <CBE  =  75 (Vertically opposite angles)

Question 10 :

Which of the following shows the fraction 13/3, 37/8 and 19/4 in order from greatest to least ?

(A)  37/8, 19/4, 13/3

(B)  37/8, 13/3, 19/4

(C)  19/4, 13/3, 37/8

(D)  19/4, 37/8, 13/3

(E)  13/3, 19/4, 37/8

Solution :

In order to arrange the fractions from greatest to least, first let us change the denominator same. For that, we have to find L.C.M of 3, 8 and 4.

L.C.M  =  24

(13/3) ⋅ (8/8)  =  104/24   -----(1)

(37/8) ⋅ (3/3)  =  111/24   -----(2)

(19/4) ⋅ (6/6)  =  114/24   -----(3)

19/4 > 37/8 > 13/3

Question 11 :

A machine launches a softball from ground level. The softball reaches a maximum height of 51.84 meters
above the ground at 1.8 seconds and hits the ground at 3.6 seconds. Which equation represents the height above ground h, in meters, of the softball t seconds after it is launched?

A) h = -t² + 3.62      B) h = -t² + 51.84

C) h = -16(t - 1.8)² - 3.6      D) h = -16(t - 1.8)² + 51.84

Solution :

By comparing with vertex form of quadratic function, we get

y = a(x - h)² + k

Here (h, k) is the maximum or minimum point.

Maximum height (k) = 51.84 m and h = 1.8 seconds

h = -16(t - 1.8)² + 51.84

Applying t = 3.6, we get

h = -16(3.6 - 1.8)² + 51.84

= -16(1.8)² + 51.84

= -51.84 + 51.84

= 0

This is the height at ground. So, option D is correct.

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