Basic Numeracy/Quantitative Aptitude

Detailed Solution

309. d: Remember the sign _x_ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive. You can try them out and find that –1 and 0 both give values less than 5 for the expression _1 – 3x_, but with 2 you get 1-6 = -5 giving an absolute value of 5. In fact there are only three integers in the solution set of this expression: -1, 0 and 1

310. a: Pick sensible numbers and work the problem out. Then go back to letters. So if 100 liters are needed per month, 20 households will need 100 x 20 liters per month. 1000 liters will last 1000/ 100 x 20 months. Putting the letters back = p/mn

311. b: The slope is the y side of the triangle divided by the x side of the triangle (y2 - y1) / (x2 - x1) This is a / 3a which is the equivalent of 1/3 but the slope is negative (because the line slopes down from left to right as we look at it). Hence -1/3

312. d: Do not attempt to work this out. Look for the pattern in the last digits in all the powers of 2. The series starts out 2...4...8...16...32....64...128..256... Already the pattern is clear; the last digits repeat in a pattern 2,4,8,6,2,4,8,6, etc. Every power that is a multiple of 4 will end in a 6 . 320 is a multiple of 4.

313. c: If the radii of the two circle are in the ratio 1 : 3, then the areas of the circle will be in the ratio (1)2 : (3)2which is 1 : 9
The marked areas represent equivalent fractions of the areas since the angles at the centers are the same. Hence the areas of the shaded parts are also in the ratio 1 : 9.
If the area of the smaller is 2, then the area of the larger will be 18.

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