ADVANCED LEVEL SCAT PRACTICE QUESTIONS

Question 1 :

The graph shows the total rainfall for six months last year in City C. 

According to the graph, what is the mean monthly rainfall?

(A) 7.5 cm    (B) 8.0 cm    (C) 9.5 cm    (D) 10.0 cm

Solution :

Rainfall in January  =  7.5, in Feb  =  4.5, in Mar  =  6, in Apr  =  9.5, in May  =  10, in June  =  8.

Mean rainfall  =  (7.5+4.5+6+9.5+10+8)/6

=  7.5

So, the mean rainfall is 7.5 cm.

Question 2 :

A set of 7 numbers has a mean of 9. What additional number must be included in this set to create a new set with a mean that is 3 less than the mean of the original set?

(A) –15    (B) –18    (C) –23     (D) –39

Solution :

Mean of 7 numbers  =  9

Sum of 7 numbers / 7  =  9

Sum of 7 number  =  63 

Sum of 8 numbers / 8  =  6

Sum of 8 numbers  =  48

The additional number  =  Sum of 8 numbers - Sum of 7 numbers

=  48 - 63

=  -15

So, the additional number is -15.

Question 3 :

Bill has 10 coins, all of which are dimes and quarters. If his dimes were quarters and his quarters were dimes, his coins would total 30 cents more. How many quarters does Bill have? 

(Note: 1 dime = $.10; 1 quarter = $.25)

(A) 2    (B) 3    (C) 4     (D) 6

Solution :

Number of coins in dime  =  x

Number of coins in quarters  =  10-x

Its value  =  0.10x + 0.25(10-x)

=  0.10x+2.5-0.25x

=  -0.15x+2.5

Quarters  =  Dimes and Dimes  =  quarters

0.25x + 0.10(10-x)  =  (-0.15x+2.5)+0.30

0.25x+1-0.10x  =  -0.15x+2.5+0.30

0.15x+0.15x  =  2.8-1

0.30x  =  1.8

x  =  1.8/0.30

x  =  6 (Number of dimes)

Number of quarters  =  4.

Question 4 :

There are 7 same-sized cups filled with water which will be used for watering plants. Fred used 1/3 of each cup of water. Janice used 1/4 of each cup of water. Approximately how many cups of water remain?

(A) 3 cups    (B) 3.5 cups    (C) 4 cups    (D) 4.5 cups

Solution :

Fred used 1/3 of each cup.

Quantity of water used by Fred  =  1/3

Quantity of water used by Janice  =  1/4

Quantity of water used by both  =  1/3 + 1/4

=  7/12

Quantity of water unused in one cup  =  1 - 7/12

=  5/12

Quantity of water in 7 cups  =  7(5/12)

=  35/12

=  2.91

So, approximately 3 cups.

Question 5 :

The area of the entire rectangle shown is 96 cm².

What is the area of the shaded region?

(A) 2 cm²      (B) 4 cm²     (C) 8 cm²      (D) 12 cm²

Solution :

In the picture given above, we have 12 rectangles having equal area.

Are of 12 equal rectangles  =  96

Area of 1 rectangle  =  96/12

=  8 cm²

So, area of the shaded rectangle is 8 cm²

Question 6 :

Which number is closest to the square root of 150?

(A) 10   (B) 12   (C) 20    (D) 75

Solution :

12²  =  144 and 13²  =  169

12² < 150 < 13²

So, the closest of square root of 150 is 12.

Question 7 :

The figures show two cubes whose volumes (V) are proportional.

What is the ratio of the side length of Figure 1 to the side length of Figure 2?

(A) 1 to 64    (B) 1 to 16    (C) 1 to 4    (D) 1 to 2

Solution :

Let a and A be the side lengths of small and large cube respectively.

Ratio of a to A  =  2 : 4

=  1 : 2

So, the required ratio is 1 to 2.

Question 8 :

Joey has a new system of currency using coins, stamps, and chips. The values are shown below.

1 coin = 2 stamps

3 chips = 2 coins

Joey is paying his friend 12 chips. How many stamps is this payment worth? 

(A) 4    (B) 6    (C) 12    (D) 16

Solution :

If 3 chips  =  2 coins, then 12 chips  =  8 coins

If 1 coin  =  2 stamps, then 8 coins  =  16 stamps

So, 12 chips worth of 16 stamps.

Question 9 :

The graph shows the relationship between the number of items ordered and the total cost of the order

Using the line of best fit, what is the average cost of a single item when 60 items are ordered?

(A) $6.67    (B) $27.50    (C) $8.33    (D) $450.00

Solution :

Average cost when 60 items are ordered 

=  (350+500+800)/60

=  $27.50

Question 10 :

If 4y – 1 = 7, then what must 8y – 2 equal?

(A) 2    (B) 8    (C) 14    (D) 16

Solution :

4y – 1  =  7

2(4y-1)  =  2(7)

8y-2  =  14

So, the answer is 14.

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