SAT I Math: a collection of medium to hard questions

This post is a collection of medium to hard SAT I Math questions of various subjects and suggested solutions. Getting the full mark in Math part is considered more easily than these other parts of SAT test. This post tries to give you some more preparation so that you won’t be surprised by and can solve tough SAT Math questions in your real test.

Question 1 (Statistics: Average): The average of 5 different integers is 25. The smallest of the 5 integers is 22. The largest of the five integers is N. How many possible values of N are there?

(A) 3        (B) 4          (C) 5        (D) 6         (E) 7

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General approach: To find the number of possible values for N, we first find maximum and minimum value that N could take.
The sum of five integers is 5x25 = 125.
Maximum value of N happens when these other four different integers take their smallest values which are 22, 23, 24, 25. Thus, max of N = 125 – (22+23+24+25) = 31.
Let N(min) be minimum value that N could take. First, straight forward, N(min) > 25. But we want to have a tighter condition for N(min). Note that maximum sum of these 5 different integers now could be: N(min) + N(min)-1 + N(min)-2 + N(min)-3 + 22 = 4xN(min) + 16. This value should be greater than or equal to 125. Thus, N(min) > 27.
Hence, N can be from 28 to 31. For each value of N in that range, we have to find the suitable values for these 3 remaining numbers before we can conclude that the value of N satisfies the question. That can be done pretty easily by balancing each value with the average value 25.
Specifically: 22 + 24 + 25 + 26 + 28 = 125
22 + 23 + 25 + 26 + 29 = 125
22 + 23 + 24 + 26 + 30 = 125
22 + 23 + 24 + 25 + 31 = 125
In summary, N could take 4 possible values (from 28 to 31). (B) is the correct answer.

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