Quant Test 99
1. Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points
P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area
inside ABCD?
4*SQRT(2)/3
2+SQRT(3)
(10-3SQRT(3))/9
1+1/SQRT(3)
2SQRT(3)-1
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2. What is the number of distinct terms in the expansion of (a + b + c)20?
231
253
242
210
228
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3. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
499
500
375
376
501
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4. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
13
21
10
15
14
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5. If the roots of the equation x3 – ax2 + bx – c =0 are three consecutive integers, then what is the smallest possible value of b?
- 1/SQRT(3)
-1
0
1
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1/SQRT(3)
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6. What are the last two digits of 72008?
21
61
01
41
81
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7. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is
perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
17.05
27.85
22.45
32.25
26.25
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8. Suppose, the seed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
= seed(s(n)), otherwise,
where s(n) indicates the sum of digits of n. For e