Question 11 :
If today is Saturday, what day of the week will it be in 365 days from now?
Solution :
The problem starts with Saturday, every 7 days from Saturday, it will be Saturday.
By dividing 365 by 7, we get 1 as remainder.So the answer will be 1 day after Saturday.
Hence the answer is Sunday.
Question 12 :
What is the remainder of 7, 700, 000, 000, 202 divided by 9 ?
Solution :
If the sum of the digits is divisible by 9, then the given number is divisible by 9.
7 + 7 + 2 + 2 = 18
Since the sum of the digits is divisible 9, the given number is divisible by 9.
Hence the remainder is 0.
Question 13 :
In the figure above AB = BC = DE = EF and the side of the square is 12. Point B and E are the midpoints of the square. Find the area of the shaded region.
Solution :
AC = 12, AE = 6
There are four semicircles.
Area of 4 semicircles with radius 6 = πr^{2}/2
= 4(πr^{2}/2) = 2 πr^{2}
= 2π(6)^{2}
= 2π(36)
= 72π
Hence the answer is 72π.
Question 14 :
8 ^{x + 3} = 64 ^{3x}, what is the value of x?
Solution :
8 ^{x + 3} = 64 ^{3x}
In order to compare the two terms, we have to convert with them having same base.
8 ^{x + 3} = (8^{2}) ^{3x}
8 ^{x + 3} = 8 ^{6x}
6x = x + 3
6x - x = 3
5x = 3
x = 3/5
Question 15 :
If A ⊏ ⊐ B = AB (A/B) - 2^{3}, then what is the value of 3 ⊏ ⊐ (6 ⊏ ⊐ 2)
Solution :
First let us calculate the value of (6 ⊏ ⊐ 2),
Instead of A we have 6 and instead of B we have 2.
(6 ⊏ ⊐ 2) = 6(2)(6/2) - 2^{3}
= 12(3) - 8
= 36 - 8
(6 ⊏ ⊐ 2) = 28
3 ⊏ ⊐ 28 = 3(28) (3/28) - 2^{3}
= 84(3/28) - 8
= 3(3) - 8
= 9 - 8
= 1
Hence the answer is 1.
Question 16 :
If the average of 11 numbers is 15, then what is the sum of these 11 numbers ?
Solution :
Average of 11 numbers = 15
Sum of 11 numbers / 11 = 15
Sum of 11 numbers = 15 (11) = 165.
Hence the required answer is 165.
Question 17 :
What is the average of (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)
Solution :
= (9b - 7) + (7 - 3b) - (-3 -3b) + (6 + 3b)
= 9b - 7 + 7 - 3b + 3 + 3b + 6 + 3b
= 9b + 3b + 9
= 12 b + 9
Average of four terms = (12b + 9)/4
= 3b + 9/4
Question 18 :
(y^{-1}⋅y^{3}⋅y^{4}⋅y^{5}⋅y^{6}) / (y^{6}⋅y^{5}⋅y^{4})
Solution :
= y^{-1 }⋅y^{3}
= y ^{(-1 + 3)}
= y^{2}
Hence the answer is y^{2.}
Question 19 :
If the pattern continues, what will be the 50^{th} symbol ?
Solution :
Each group consists of 6 different symbols and it ends with the symbol upside arrow.
Let us divide 50 by 6, we get the remainder 2. Hence the 50^{th} place should be filled with the symbol heart.
Question 20 :
A trapezoid has base length in the ratio of 2 : 6. If the area of a trapezoid is 260 and altitude is 5, then what is the length of longer side ?
Solution :
Area of trapezoid = (1/2) ⋅ h ⋅ (a + b)
Here, a = 2x, b = 6x and altitude (h) = 5
(1/2) ⋅ 5 ⋅ (2x + 6x) = 260
(5/2)(8x) = 260
x = 260/20
x = 13
2x = 2(13) = 26, 6x = 6(13) = 78
Hence the longer side is 78.
More Practice Test Papers
SHSAT math practice test - Paper 1
SHSAT math practice test - Paper 2
SHSAT math practice test - Paper 3
SHSAT math practice test - Paper 4
SHSAT math practice test - Paper 5
SHSAT math practice test - Paper 6
SHSAT math practice test - Paper 7
SHSAT math practice test - Paper 8
SHSAT math practice test - Paper 9
SHSAT math practice test - Paper 10
SHSAT math practice test - Paper 11
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