GMAT Tough Problem Solving - 9(Numbers, Percentage , Profit and Loss)

41. How many 3-digit numerals begin with a digit that represents a prime and end with a digit that represents a prime number?


A) 16 B) 80 c) 160 D) 180 E) 240

42. There are three kinds of business A, B and C in a company. 25 percent of the total revenue is from business A; t percent of the total revenue is from B, the others are from C. If B is $150,000 and C is the difference of total revenue and 225,000, what is t?


A.50 B.70 C.80 D.90 E.100

43. A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 40% are drinking beer, 40% are drinking mixed drinks, and 20% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?


A. 2/5

B. 4/7

C. 10/17

D. 7/24

E. 7/10

44. A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?


A) 20% B) 40% C) 50% D) 60% E) 75%

45. If the first digit cannot be a 0 or a 5, how many five-digit odd numbers are there?


A. 42,500

B. 37,500

C. 45,000

D. 40,000

E. 50,000

Solutions

41.Soln: The first digit can be 2, 3, 5, or 7 (4 choices)

The second digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 (10 choices)

The third digit can be 2, 3, 5, or 7 (4 choices)

4 * 4 * 10 = 160

42.Soln: Let the total revenue be X.

So X= A + B+ C

which is X= 1/4 X+ 150 + (X-225)

4X= X+ 600 + 4X -900

Solving for X you get X= 300

And 150 is 50% of 300 so the answer is 50 % (A)

43.Soln: The probability of an event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes.The total number of possible outcomes is the total percent of students drinking beer.40% of the students are first year students. 40% of those students are drinking beer. Thus, the first years drinking beer make up (40% * 40%) or 16% of the total number of students.


60% of the students are second year students. 30% of those students are drinking beer. Thus, the second years drinking beer make up (60% * 30%) or 18% of the total number of students.


(16% + 18%) or 34% of the group is drinking beer.


The outcomes that result in A is the total percent of students drinking beer and mixed drinks.


40% of the students are first year students. 20% of those students are drinking both beer and mixed drinks. Thus, the first years drinking both beer and mixed drinks make up (40% * 20%) or 8% of the total number of students.60% of the students are second year students. 20% of those students are drinking both beer and mixed drinks. Thus, the second years drinking both beer and mixed drinks make up (60% * 20%) or 12% of the total number of students.(8% + 12%) or 20% of the group is drinking both beer and mixed drinks.If a student is chosen at random is drinking beer, the probability that they are also drinking mixed drinks is (20/34) or 10/17.

44.Soln: Lets suppose original price is 100.

And if it sold at 20% discount then the price would be 80

but this 80 is 120% of the actual original price...so 66.67 is the actual price of the item now if it sold for 100 when it actually cost 66.67 then the gross profit would be 49.99% i.e. approx 50%

45.Soln: This problem can be solved with the Multiplication Principle. The Multiplication Principle tells us that the number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event.

There are 8 possibilities for the first digit (1, 2, 3, 4, 6, 7, 8, 9).

There are 10 possibilities for the second digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

There are 10 possibilities for the third digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

There are 10 possibilities for the fourth digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

There are 5 possibilities for the fifth digit (1, 3, 5, 7, 9)


Using the Multiplication Principle:


= 8 * 10 * 10 * 10 * 5

= 40,000

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