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Q1A box contains tickets numbered 01 to 100.<br/><br/>What is the probability that a ticket selected at random will have number with a tenth digit of 5?
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✓ Correct answer: 1/10
The tenth digit of 5 is 05, 15, 25 ....., and 95. i.e. 10 possible numbers out of 100 numbers.Probability P = favourable events for success / total possible events = 10/100 = 1/10.<br/><br/><b>Key takeaway: </b>Probability is the chance of the occurrence of an event. It is the ratio of favourable events for success and total possible events.
Q2Rectangular floors X and Y have equal area. If floor X is 8 feet by 27 feet and floor Y is 9 feet wide, what is the length of floor y, in feet?
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✓ Correct answer: 24
Area of rectangle = length X width, 8X27=9Xw, w= (8X27)/9=24<br/><br/><b>Key takeaway: </b>Area of rectangle is equal to the product of its length and width. Compare two geometrical figures to find out missing information.
Q3Which of the following is greater than 1/3?
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✓ Correct answer: 4/11
You can change numerator of 1/3 by multiplying both numerator and denominator by the same numbers.<br/>1/3 = 33/99 , 4/12, 3/9 and 5/15<br/><br/>33/100 <33/99<br/><br/>4/11 >4/12<br/><br/>3/10 < 3/9<br/><br/>5/16 <5/15<br/><br/>4/11 is greater than 1/3<br/><br/><b>Key takeaway:</b> The GMAT often asks you to compare two or more fraction and decide which is larger. Use the Bowtie technique to find the common denominator. This technique is also used to add or subtract. Compare the first two fractions and eliminate the smaller one and then compare with next fraction; and so on.
Q4If x=5 and y=-5, what is the value of y2 - 2y + 2x?
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✓ Correct answer: 45
It is simply putting values with due care of positive and negative signy<sup>2</sup> - 2y + 2x = (-5)<sup>2</sup> - 2(-5) +2 (5) = 25 +10+10 = 45<br/><br/><b>Key takeaway: </b>Remember four simple rules of multiplication of positives (+) and negative (-) numbers.<br/><br/>Pos x pos = pos 2x3 = 6<br/><br/>Neg x neg = pos -2 x -3 = 6<br/><br/>Pos x neg = neg 2 x -3 = -6<br/><br/>Neg x pos = neg -2 x 3= -6.
Q5What is the smallest integer n for which 16n = 412?
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✓ Correct answer: 6
First convert 16<sup>n </sup>to the same base 4. You know 16 = 4 x 4 = 4<sup>2</sup> , so you can write 16<sup>n </sup>= (16)<sup>n </sup>= (4<sup>2</sup>)<sup>n</sup> = 4<sup>2n</sup>. We know that given 16<sup>n</sup> = 4<sup>12</sup>, so we can write 4<sup>2n</sup> = 4<sup>12</sup> Since both have ase 4, their powers are equal 2n = 12, or n = 6.<br/><br/><b>Key takeaway: </b>When solving problems involving exponents, base is to be seen carefully. It is easy to simplify, as long as they have the same base. Remember following simple formulae:a<sup>m</sup> x a<sup>n </sup>= a<sup>m+n</sup>, a<sup>m</sup> / a<sup>n</sup> = a <sup>m-n</sup> , (a<sup>m</sup> ) <sup>n</sup> = a <sup>m x n</sup> , (a<sup>m </sup>) <sup>1/n</sup> = a <sup>m/ n</sup>
Q6A contractor planned to cover a floor measuring 6.5 feet by 11.8 feet. Realizing that there would be a cabinet covering 2 square feet of the floor at one end of the room, he decided not to cover that portion of the floor. Since the floor covering is only available in multiples of 5 square feet, which amount should he order?
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✓ Correct answer: 75 sq. ft.
6.5 x 11.8 = 76.7 square feet Subtract the 2 square feet not being covered and get 74.7 square feet. To cover this area, the contractor would have to go up to the next even 5 square foot amount, which is 75.
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