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GMAT Questions
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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.
Q7A rectangular field ABCD has a flower garden which is 18 feet by 6 feet. If the garden covers 30 percent of the field, what is the area, in square feet, of the field?
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✓ Correct answer: 360
The area of the garden is equal to 18X6=108, garden is 30% of the field. As 30% is equal to 108, 100% is equal to 108/30X100=360.<br/><br/><b>Key takeaway: </b>Area of rectangle is equal to length X width. Questions based on area of standard geometrical figures such as rectangle, square, triangle, circle, etc are asked. List out their formulae and practice over them.
Q8The total cost of food for the raccoons at the Altadena Wildlife Rescue has increased as the number of raccoons at the Rescue has increased. If it costs the same amount to feed each raccoon, is the cost of food for 7 raccoons more than $2,000 annually?<br/><br/>(1) It costs more than $1,000 annually to feed 4 raccoons.<br/><br/>(2) It costs more than $1,500 annually to feed 5 raccoons.
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✓ Correct answer: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(1) If it costs more than $1,000 annually to feed 4 raccoons, we do not have enough information to answer either yes or no to the original question. It could cost $2,000 to feed 4 raccoons, in which case it WOULD cost more than $2,000 to feed 7 raccoons. Or, it could cost only $1,000 and one cent to feed 4 raccoons, in which case feeding 3 more would be less than an additional $1,000, and the answer would be no. This statement is insufficient.<br/><br/>(2) If it costs more than $1,500 annually to feed 5 raccoons, then the smallest cost for each animal is a little over $300. $300 x 7 raccoons = $2,100. Sufficient.
Q9During a two-month period, the price of a gallon of gas increased by 15% after the first month and then decreased by 10% of this new price at the end of the second month. If the price of gas was <em>y</em> dollars per gallon at the beginning of the two-month period, what was the price, in dollars per gallon, by the end of the period?
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✓ Correct answer: 1.035<em>x</em>
At the end of the first month, the price of a gallon of gas was 1.15x. At the end of the second month, the price was 10% less than 1.15x, or (0.90)(1.15x) = 1.035x.
Q10A baseball coach wants to schedule an extra 1-hour practice on Saturday for players <em>A</em>, <em>B</em>, <em>C</em>, and <em>D</em>. Is there a one-hour period on Saturday that is open for all four players?<br/><br/>(1) On Saturday, <em>A</em> and <em>B</em> are free from 1:00 p.m. to 4:00 p.m.<br/><br/>(2) On Saturday, <em>C</em> is free from 2:00 p.m. to 5:00 p.m. and <em>D</em> is free from 12:00 noon to 3:00 p.m.
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✓ Correct answer: Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
To have sufficiency, you will need to know when each of the players is free.<br/><br/>Statement (1) alone is insufficient because it only gives information about players A and B. Eliminate choices (A) and (D).<br/><br/>Similarly, statement (2) alone is insufficient because it only has information regarding players C and D. Eliminate choice (B).<br/><br/>Statements (1) and (2) together have information about the open periods of all four players. From these two statements, you can determine that all four players are free from 2:00 p.m. to 3:00 p.m. Statements (1) and (2) together are sufficient and the answer must be choice (C).
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