Basic Numeracy/Quantitative Aptitude

Detailed Solution

129. d: Let a and b be the two sides of the triangle such that a is longer than b. The statement "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle" may be fomulated by
h = a + 2 or a = h - 2
The statement "the shorter side of the triangle is 7 centimeters less than the longer side" may be fomulated .
b = a - 7 or b = (h - 2) - 7 = h – 9

Only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle.

130. b: The difference between two odd integers is equal to 2. let x be an odd integer and x + 2 be its consecutive. The sum of x and twice its consecutive is equal to 3757 gives an equation of the form
x + 2(x + 2) = 3757
Solve for x
x = 1251
Check that the sum of 1251 and 2(1251 + 2) is equal to 3757.

131. a: Let x, x + 2 and x + 4 be three integers. The sum of the first x and third x + 4 is given by
x + (x + 4)
131 less than three times the second 3(x + 2) is given by
3(x + 2) - 131
"The sum of the first and third is 131 less than three times the second" gives x + (x + 4) = 3(x + 2) - 131
Solve for x and find all three numbers
x = 129 , x + 2 = 131 , x + 4 = 133

132. b: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two x + (x + 2) twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 742 is written as x + (x + 2) + 4 x + 20 = 742
Solve for x and find all four numbers
x = 120 , x + 2 = 122 , x + 4 = 124 , x + 6 = 126

133. c: Let x, x + 2 and x + 4 be the three integers. "The smallest added to four times the largest is written as follows"
x + 4 (x + 4)
"729 more than four times the middle integer" is written as follows 729 + 4 (x + 2)
"When the smallest is added to four times the largest, it produces a result 729 more than four times the middle" is written as follows
x + 4 (x + 4) = 729 + 4 (x + 2)
Solve for x and find all three numbers
x + 4 x + 16 = 729 + 4 x + 8
x = 721
x + 2 = 723
x + 4 = 725
Check: the smallest is added to four times the largest 721 + 4 * 725 = 3621
four times the middle
4 * 723 = 2892
3621 is more than 2892 by
3621 - 2892 = 729

134. d: The absolute decrease is
20 - 15 = $5 The percent decrease is the absolute decrease divided by the the original price (part/whole).
percent decease = 5 / 20 = 0.25
Multiply and divide 0.25 to obtain percent.
percent decease = 0.25 = 0.25 * 100 / 100 = 25 / 100 = 25%

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