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hair (2) Adding a, b, c, and d, we get 9 + 3 + 5 + 2 = 19.
    21.   (d)
    It is very tempting to just subtract the times 9:09 from 10:10, etc., and get 61 minutes, or if you’re careless get 101 minutes. However, think of the times closest to one another, 12:12 and 1:01, and you will find the difference is 49 minutes.
    22.   (c) 5
    Draw lines to see that BD is a radius of the circle. The two diagonals of a square will have the same length.
    23.   (a) 25 x 25 x 25 x…(where there are fifty 25s)
    Try to find a connection between the numbers. You are comparing 50 x 50 x 50 x 50…(100 times) to 100 x 100 x 100 x 100… (50 times). Write 100 as 50 x 2, so now you are comparing 50 x 50 x 50 x 50…(100 times) to 50 x 2 x 50 x 2 x 50 x 2 x 50 x 2.(50 times).You can now cancel 50 x 50 x 50 x 50.50 times from both sides of the comparison. You would then get 50 x 50 x 50 x 50.(50 times) compared with 2 x 2 x 2 x 2.(50 times). You can see the left side of the comparison is 25 x 25 x 25 x 25…(50 times) times the right side.
    24.   Say IN means NOT, then associate EXTRIC with another word, EXTRACT. So INEXTRICABLE means not extractable—incapable of being extracted—or INSEPARABLE. Association is a powerful strategy for getting the meaning of words.
    25.   The doctor is the son’s mother.
    26.   If many people paid attention to the ad, it would be very crowded in the early hours. Of course the reason why the ad was put in was because the store did not think that so many people would read the ad.
    27.   (b) second
    Many people who get this problem wrong think of just the numbers, not the wording, assuming that if you overtake the second runner, you are first. But when you overtook the second runner, you took his or her place. Therefore you are now in second place, not first place.
    28.   (e) none of the above
    If the four daughters are those mentioned, think of who the fifth daughter could be—the fifth daughter is Bonnie herself.
    29.   (e) thimble : finger
    Create a sentence expressing a specific relationship between the capitalized words. HELMET is worn on the HEAD to protect the head, as THIMBLE is worn on the FINGER to protect the finger.
    30.   If a number is an exact multiple of 9, the sum of the digits of that number is also a multiple of 9. So 1 + 2 + 3 + x = 9 and x = 3.
    31.   The knight could tear up the paper he picks and offer the other one to the king. He could then tell the king that since the untorn paper reads “Death,” the one torn must have read, “Marriage.”
    32.   From first to last: John, Mary, Sarah, Barry
    The easy way to find the answer is to draw the situation with labels for the people’s names.
    (1) Sarah is between Barry and Mary: B S M or M S B.
(2) John is directly in front of Mary: J M
(3) Mary is in front of two other people: M S B
    So we get from (2) and (3): J M S B
    33.   One-half the surface area of a ball is greater. Blow up the circle like a balloon to get the ball. One half the surface area of the ball is greater than the area of the circle because the circle is being expanded by being blown up.
    34.   Write a three-digit number with h hundreds digit, t tens digit, and u units digit as 100 h + 10 t + u . You will find that A = 1, B = 0 and C = 9.
    We have 100A + 10B + A - 10C - A = 10A + B. This gives us 90A + 9B = 10C or 10A + B = (10/9)C.
    The only way A and B can be integers is if C = 9. That makes 10A + B = 10. The only way this is possible with A and B as integers (from 0 to 9) is if A = 1 and B = 0.
    35.   (b) m
    Letters are arranged in pairs, backward skipping every third letter: m n (o) p q (r) s t (u) v w (x) y z.
    36.   5
    Draw a perpendicular line to make a rectangle in the figure and you will also have a 3-4-5 triangle.

    A powerful strategy in geometry is to draw extra lines to get more information from the problem. You may not remember this, but when you first took geometry, one of the first proofs that the teacher probably