PLUGGING IN AND PITA DRILL 2 EXPLANATIONS
3 . A If you’re not sure how to factor this expression, choose a value for a and find the value of the
expression. Then substitute the same value for a to see which of the answer choices has the
same value. Try an easy number to avoid complicated calculations, such as a = 2. In the
original expression, a^2 − 8a + 16 = (2)^2 − 8(2) + 16 = 4 − 16 + 16 = 4. When you plug a = 2
into each of the answer choices, only (A) gives a value of 4: (2 − 4)(2 − 4) = (−2)(−2) = 4.
6 . K The question asks for the length of the longest piece of string, so use the provided answers as
a guideline. Start in the middle with (H), so the longest piece of string would be 18
centimeters. The second piece of string would be half that length, or 9 centimeters. The third
piece of string is one-third the length, or 3 centimeters, and the fourth piece is one-third of
that, or 1 centimeter. The sum of these lengths would be 18 + 9 + 3 + 1 = 31, which does not
agree with the 62 centimeters given in the question. Eliminate (F) and (G), which will also
be too low. With (K), the longest piece of string would have a length of 36 centimeters, the
second piece would be 18 centimeters, the third would be 6 centimeters, and the fourth
would be 2 centimeters. The total length of all four pieces would be 36 + 18 + 6 + 2 = 62,
which agrees with the total given in the question.
7 . C Because the distributing in this problem can be difficult, try picking a few values. Keep them
simple: let’s say w = 2, x = 3, y = 4, and z = 3. In the given expression, this will mean −2[3 −
(4 + 5)] = −2[3 − 9] = −2[−6] = 12. Plug these numbers in to the answer choices to see
which gives a value of 12. Only (C) works, so it is the correct answer.
9 . C You can use the answer choices to help solve this question. If you start with (C), the sequence
of numbers would be 5, 17, 29, 41, 53. According to the question, the difference between
consecutive numbers should remain the same. So, since 17 − 5 = 12, all the other differences
between consecutive numbers should also be 12: 29 − 17 = 12, 41 − 29 = 12, and 53 − 41 =
12, so this is the correct answer. The other choices each have the same difference between
the three numbers in the choices themselves, but none of them carries that difference to the 5
and 53 given in the problem. Make sure that you check every pair of consecutive numbers
when trying each answer choice, and don’t forget the numbers from the problem!
18 . G To find the smallest number of cards that all three can buy, use the answer choices. The
correct answer will need to be divisible by 10, 15, and 25. Remember, though, that even if an
answer choice works, you need to find the smallest number, so start with (F). Since 25 is not
divisible by either 10 or 15, (F) is not correct. Choice (G) is divisible by 10, 15, and 25, so
it is the answer. Choices (H), (J), and (K) are larger than (G), so it is irrelevant whether they
are divisible by our numbers or not.
