To find questions from 1 to 5, please visit the page "SHSAT Math Practice for 9th Graders"
To find questions from 6 to 10, please visit the page "SHSAT Math Test with Answers"
Question 11 :
The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have?
(A) 55 (B) 40 (C) 39 (D) 13 (E) 9
Solution :
If the the largest number be 55, then the sum of other 6 numbers be 11. So, it is not possible.
If the the largest number be 40, then the sum of other 6 numbers be 21.
The possible 6 numbers are 1, 2, 3, 4, 5, 6 which are unequal and gives the sum 21.
Question 12 :
In the set {1, 5, x, 10, 15}, the integer x is the median. The mean of the five numbers is one less than x. The value of x is
(A) 6 (B) 7 (C) 8 (D) 9 (E) none of these.
Solution :
Mean of 5 numbers = (1 + 5 + x + 10 + 15)/5
x - 1 = (31 + x)/5
5(x - 1) = 31 + x
5x - 5 = 31 + x
5x - x = 31 + 5
4x = 36
x = 9
Hence the required value of x is 9.
Question 13 :
If 7/50 < 1/x < 8/51 where x is an integer, then x =
(A) 8 (B) 7 (C) 6 (D) 5 (E) 4
Solution :
7/50 < 1/x < 8/51
7x < 50 7x < 7 1/7 x < 7 1/7 |
1/x < 8/51 51 < 8x 6 3/8 < 8x 6 3/8 < x |
By combining these two inequalities, we get
6 3/8 < x < 7 1/7
Since x must be an integer, the value of x is 7.
Question 14 :
Half of 2^{8} is
(A) 2^{7} (B) 2^{6} (C) 2^{4} (D) 1^{8} (E) 8
Solution :
= Half of 2^{8}
= (1/2) ⋅ 2^{8}
= 2^{7}
Hence the answer is 2^{7}.
Question 15 :
If x is greater than 1/2 but less than 1, which of the following has the largest value?
(A) 2x – 1 (B) x^{2} (C) 1/x (D) 1 – x (E) x^{3}
Solution :
1/2 < x < 1
Let us test option A :
Multiply 2 through out the inequality
1 < 2x < 2
Subtract 1,
0 < 2x - 1 < 1
The value of 2x - 1 lies between 0 and 1.
Option B :
1/2 < x < 1
Taking squares,
1/4 < x^{2} < 1
Option C :
1/2 < x < 1
Taking reciprocals,
2 < 1/x < 1
The value of 1/x lies between 1 and 2.
Option D :
1/2 < x < 1
Subtract 1,
1 - 1/2 < 1 - x < 1 - 1
1/2 < 1 - x < 0
The value of 1 - x lies between 0 and 1/2.
Option E :
1/2 < x < 1
1/8 < x^{3} < 1
Hence the largest value is between 1 and 2. So, option C is correct.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Dec 02, 22 04:18 PM
Dec 02, 22 07:27 AM
Dec 02, 22 07:16 AM