SAT Math: Some More Picking Numbers Problems

Our first post, written ten months ago, had to do with a very important SAT Math strategy: Picking Numbers.  If you’d like some more practice on this type of problem, here are seven more that you can try.  The answers appear at the bottom of this post.

1)  In rectangle ABCD, Point E lies 4/7 of the way from A to B.  The area of triangle EBC is what fraction of the area of rectangle ABCD?

Picking Numbers 1

(A)  3/14
(B)  2/7
(C)  3/7
(D)  3/8
(E)  4/7

2)  When x + 1 is divided by 5 the remainder is 4.  What is the remainder when 3x + 2 is divided by 5?

(A)  0
(B)  1
(C)  2
(D)  3
(E)   4

3)  If the number m + 2 is a perfect square (that is, the square of a whole number), which of the following must also be a perfect square?

(A)  4m
(B)  4m + 4

(C)  4m + 9
(D)  6m + 12
(E)   9m + 18

4)  When a is divided by 7, the remainder is 4 and when b is divided by 7, the remainder is 5.  What is the remainder when the product ab is divided by 7?

(A)  0
(B)  2
(C)  4
(D)  5
(E)  6

5)  John bought a new car.  Two years later he sold it back to the dealer for 30% less than the amount he originally paid for the car.  The dealer then added 15% to the amount he paid to John for the car and resold it to Sarah.  The price that Sarah paid for the car is what percent of the original price that John paid?

(A)  75
(B)  77 .5
(C)  80.5
(D)  82.5
(E)   85

6)  If x2 = m + 2, then what is the difference between x4 and x2, in terms of m?

(A)  m + 2
(B)  m + 4
(C)  m2 + 4
(D)  m2 + 3m + 2
(E)   m2 + 4m + 4

7)  The first term in an arithmetic sequence is a.  Each term after the first is x more than twice the preceding term.  What is an expression for the fourth term of the sequence in terms of a and x?

(A)  2a + x
(B)  4a + 2x
(C)  4a + 3x
(D)  8a + 7x
(E)   8a + 8x

To try a few more of these problems, go here.

Questions about this strategy or anything else related to the SAT?  Leave a comment or send me an email at

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


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