1.Correct Answer: E
Explanation:
Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.
2.Correct Answer: B
Explanation:
We can write the statement mathematically, using x to mean ‘of’ and /100 for ‘per cent’. So ( √5/100) x 5√5 = 5 x 5 /100 = 0.25
3.Correct Answer: D
Explanation:
If pqr = 1, none of these variable can be zero. Since spr = 0 , and since p and r are not zero, s must be zero. (Note that although rst = 0, and so either s or t must be zero, this is not sufficient to state which must be zero)
4.Correct Answer: E
Explanation:
65 = 64x 6
(64 x 6) - 64 = 64(6 - 1) = 64 x 5
Now, dividing by 5 will give us 64
5.Correct Answer: E
Explanation:
All terms in the sequence will be multiples of 4.
762 is not a multiple of 4
6.Correct Answer: A
Explanation:
Choice I is correct because f(x) = 6 when x=3
Choice II is incorrect because to make f(x) = 0, x2 would have to be 3. But 3 is not the square of an integer.
Choice III is incorrect because to make f(x) = 0, x2 would have to be –3 but squares cannot be negative.
(The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)
7.Correct Answer: C
Explanation:
1
n can be 0, or -1
n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
The largest value for n will be an integer
193/4 = 48.25, hence 48
The number of integers between -1 and 48 inclusive is 50
8.Correct Answer: B
Explanation:
First you must realize that the sum of two 2-digit numbers cannot be more that 198 (99 + 99). Therefore in the given problem D must be 1.
Now use trial and error to satisfy the sum 5A + BC = 143
A + C must give 3 in the units place, but neither can be 1 since all the digits have to be different. Therefore A + C = 13.
With one to carry over into the tens column, 1 + 5 + B = 14, and B = 8.
A + C + B + D = 13 + 8 + 1 = 22
9.Correct Answer: B
Explanation:
Total volume of water = 12 liters = 12 x 1000 cm3
The base of the aquarium is 50 x 30 = 1500cm3
Base of tank x height of water = volume of water
1500 x height = 12000; height = 12000 / 1500 = 8
10.Correct Answer: A
Explanation:
Let Ben’s age now be B
Anita’s age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B
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