X is the sum of all the even positive integers less than or equal to 50.Y is the sum of all the odd positive integers less than or equal to 49.Quantity AX - YQuantity B25
Answer(s): C
X is 2 + 4 + ... + 50, an arithmetic series with 25 terms.Y is 1 + 3 + ... + 49, also 25 terms.X - Y = 650 - 625 = 25, exactly the same as Quantity B, so the two quantities are equal.
x > -1Quantity AQuantity B
Answer(s): D
Because 81 is positive, the one with the larger value depends only on the sign of x3.If
Quantity Aat + sbQuantity Brc
The altitude r splits the triangle into two right triangles whose areas areTogether they make the whole triangle, whose area isat + sb = rc.
Quantity AyQuantity B1
Answer(s): B
By the Law of Cosines on the side 2 opposite the angle x,2 = 1 + y2 - 2y cos x.Because x > 90°, cos x is negative, so the term -2y cos x is positive. Hence 2 > 1 + y2, which simplifies to y2 < 1 and therefore y < 1.
A certain group of 10 people consists of 5 men and 5 women. From this group, 2 people are to be selected at random. The probability that the 2 people selected will consist of 1 man and 1 woman is equal to p.Quantity ApQuantity B
Answer(s): A
5 × 5 = 25
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