Star's_general Good Problems

12. Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine M, working along at its constant rate, to produce all of the units produced last Friday? (A) 8 (B) 12 (C) 16 (D) 24 (E) 30 27. For each landscaping job that takes more than 4 hours, a certain contractor charges a total of r dollars for the first 4 hours plus 0.2r dollars for each additional hour or fraction of an hour, where r>100. Did a particular landscaping job take more than 10 hours? (1) The contractor charges a total of $288 for the job (2) The contractor charges a total of 2.4r dollars for the job. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. (D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient. A circle is centered on the origin in the coordinate plane. Point (A, B) is randomly selected inside of the circle. What is the approximate probability that A > B > 0? A. 1/8 B. ¼ C. 3/8 D. ½ E. ¾ (A) Since the circle is centered on the origin, exactly 1/4 of the points in the circle will consist of points where both x and y are positive (those in Region I in the coordinate plane). Of these points, half will lie above the line y = x (where y > x) and half will lie below it (where x > y). Thus, 1/8 of the circle will consist of all the points in which x > y > 0.The correct answer is choice (A). Q: Your answer: C Right answer: E What is the value of x? (1) y² = x (2) (x + 4)/4 = y + 1

What out for the equations with square while solving. You just cant assume that you will get a single answer. Q: Your answer: B Right answer: E A shuttle bus traveled to its daily destination city at an average speed of 60 kilometers per hour. On the return trip, the bus traveled the same distance, but at an average speed of only 40 kilometers per hour, making the trip 4 hours longer. What is the total distance of the round trip? A. 360 kilometers B. 480 kilometers C. 600 kilometers D. 720 kilometers E. 960 kilometers Read the question. What is asked. Total distance of the round trip and not just the distance. Don’t make such kind of stupid mistakes. Question 35. Your answer: C Right answer: B Does 8x = 16 + 2x? (1) -3x is greater than or equal to -9. (2) 2x is greater than or equal to 6. Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied during a certain show? (1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row for the front 20 rows. (2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row for the back 15 rows. 22 If X^2+Y^2=1, is X+Y=1? (1) XY=0 (2) Y=0 32

If ¼ of the larger of two numbers is greater than 5 times the smaller of the same two numbers, is the smaller number less than 4? (1) The larger number is greater than 70. (2) The larger number is less than 80 Question 12. Your answer: D Right answer: A If r and s are both positive integers, is the product of r and s even? (1) (r + 3) is a prime number (2) (s + 1) is a prime number.

Question 13. Your answer: B Right answer: D If a and b are odd integers such that a – b > 7, what is the least possible positive difference between a and an even number less than b? A. 6 B. 7 C. 8 D. 9 E. 10 Q Maths test 2 800score problem 25 ( refer for figure) As shown in the figure above, line segments AB and AC are tangent to circle O. If line segments BD and DA have the same length, what is the degree measure of angle BAO? (Note: Figure not drawn to scale.) A. 15º B. 30º C. 36º D. 45º E. 50º Question 30.Your answer: A Right answer: D Crew A can build a car in 20 minutes and Crew B can build a car in 25 minutes. If both crews work independently and start at the same time, what is the least amount of time required for the two crews to build 10 cars? A. 111 1/9 minutes B. 115 2/5 minutes C. 116 minutes D. 120 minutes E. 125 minutes Above problem is a good problem Q35. Linda purchased 3 books at a book fair. What was the median price of the 3 books? (1) The average (arithmetic mean) price of the 3 books was $1.5 (2) The price of one of the 3 books was $1.5

Q7: If y is an integer and y = |x| + x, is y = 0? (1) x < 0 (2) y < 1

Q10: What is the hundreds digit of the integer z? (1) 10z = 93,120 (2) z rounded to the nearest hundred is 9,300.

Q:

One kilogram of a certain coffee blend consists of x kilogram of type I and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C=6.5x + 8.5y. Is x < 0.8? (1) y > 0.15 (2) C >= 7.30 Q:

800score test 3.

Your answer: C Right answer: A The table above shows quantities of various mobile phone models sold by a retailer. Assuming prices did not change between 2003 and 2004, was the company’s total revenue from sales of these models in 2004 greater than its total revenue from sales of these models in 2003? (1) Model A was the most expensive phone. (2) Model C was the least expensive phone.

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Q6: A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is the value of n? (1) The probability that the two bulbs to be drawn will be defective is 1/15. (2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

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Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is

numbered 5 ?

Question 10. Your answer: A Right answer: D If N is a positive integer, what is the units digit of the sum of the following series: 1! + 2! + ... + N!? (The series includes every integer between 1 and N, inclusive) (1) N is divisible by 4. (2) (N² + 1)/5 is an odd integer. Question 7. Your answer: E Right answer: B What is the two-digit positive integer whose tens digit is a and whose units digit is b? (1) 2a > 3b > 6 (2) a > 2b > 6.

Question 5. Your answer: E Right answer: A The vertices of a triangle are at coordinates (-2, 1), (3, 1), (x, y) on a rectangular coordinate plane. What is the area of the triangle? (1) |y – 1| = 1 (2) The interior angle at vertex (x, y) measures 90 degrees.

Question 19.Your answer: C Right answer: E The graph on the left shows the average salary per employee for various years of operation of a company. The graph on the right shows the number of employed workers each of these years. If, in 2003, 1300 of the company’s employees were each paid $40,000, and no employee was paid less than $39,000, which of the following is the maximum salary that could have been paid by the company in 2003? A. $50,000 B. $55,000 C. $64,000 D. $72,000 E. $89,000

Question 31.Your answer: C Right answer: B A group of numbers, S, contains more than one element. Is the range of group S larger than the mean? (1) Group S does not contain positive elements. (2) The mean of group S is negative.A .(B) We must remember that this group can have multiple elements with the same value. From Statement (1), we can determine that the mean of S is not positive. It can be zero or negative. Because the range of any set is zero or a positive value, either mean = range = 0 (in which case the answer to the above question is NO) or the range is positive and the mean is less than 0 (in which case the answer is YES). So Statement (1) is insufficient.From Statement (2), we know that at least one of the elements is negative, since the mean is negative. Therefore, we know that the smallest value in the set must be negative. Also the mean can never be greater than the largest number in the set.Range is equal to:Largest Value – Smallest Value.Since the smallest value must be negative, the range will be larger than the largest value. This is because subtracting a negative number is the same as adding the positive of the number.Since the range is greater than the largest number, and the largest number must be greater than the mean, we know that the range is greater than the mean. Therefore, Statement (2) is sufficient.If this seems too abstract, it helps to pick some numbers, like the set {-5, -4, 2} to show how the range will be greater than the mean. The mean is negative, and the range is 2 – (-5) = 7.Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).

A cubical box with an edge length of 4 inches holds a ball with a radius of 2 inches, such that the ball touches the box on all six sides. What is the distance, in inches, between the center of the ball and a corner of the box? A. 6√3 B. 4√3 C. 2√3 D. 2√2 E. √2 Your answer: D Right answer: D A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. Exactly 61% preferred brand A and exactly half as many preferred brand B. Only 65 chose brand C. Which of the following could be the number of customers who preferred brand D? A. 8

B. 11 C. 14 D. 20 E. 31 (D) 61% preferred A and 30.5% preferred B, so the number that preferred either C or D must be 8.5% of the total. If n is the number of people customers who were surveyed, 8.5n/100 = 17n/200 preferred either C or D. Thus we know that 17n/200 > 65, as the choices make it clear that some people preferred brand D. However, we also know that since 17n/200 is an integer and 17 is a prime number, n must be a multiple of 200, i.e. n = 200k for some integer k. Therefore we can write the above inequality as k > 65/17. Thus k must be at least 4. If k is 4, the number of people who prefer either C or D would be 68, 68 – 65 = 3 of which would prefer D. If k= 5, the number of people who prefer either C or D would be 85 , 20 of which would prefer D. Thus 20 could be the number of people who prefer brand D.

This is a very simple problem but you had to think a lot when you attempted it first time.

Q: Is p + q > r + s 1. p > r + s 2. q > r + s This is a good trap problem. Solve… E…. Think how…