Problem Solving

nothinglessthan780 wrote:Anyone who can help me solve these questions please!Sorry they are quite a number of questions.


Q2)
If the operation @ is defined for all integers a and b by a@b=a+b-ab,which of the following statements must be true for all integers a,b and c
I)a@b=b@a
II)a@0=a
III)(a@b)@c =a@(b@c)

for I. a + b - ab = b + a -ba
True
II. a + 0 - a * 0 = a
True
III. (a+b-ab) + c - c(a+b-ab) = (b + c - bc) + a - a( b+c-bc)
True

Q3)
The function f is defined for all positive integers n by the following rule.f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1.If p is any prime number than f(p)=

A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2

by definition, a prime number has no factors other than one and itself in common with any other number. However, since we're only looking at numbers below the prime number, one is the only factor that a prime number can share with a number below it. Therefore f(p) = p-1, as a prime number shares no factors with any number below it. f(17) =16, f(13) = 12 and so on

Q4)
The y-intercept of line l is 4.If the slope of l is negative,which of the following couldbe the x intercept of l?
I)-1
II)0
III)6

draw a line with a negative slope that intersects the y axis at (0, 4). X must be positive when it intersects the x axis since as the x increases, y decreases if a line has a negative slope.

Q5)
A college admissions officer predicts that 20% of the students who are accepted will not attend the college.According to this prediction,how many students should be accepted to achieve a planned enrollment of x students?

If 20% will not attend the college, 80% or 4/5 of students will attend the college. In order to achieve an enrollment of x, (5/4)x students must be admitted so that (5/4)x * 4/5 or x students will attend the college.


Q6)
For any positive integer n, the length of n is defined as the number of prime factors whose product is n.For example the length of 75 is 3 since 75=3*5*5.How many two digit positive integers have length 6?

Start with six two's, since its the lowest integer that can produce a 2 digit integer.

2*2*2*2*2*2 = 64
2*2*2*2*2*3 = 96

These only two-digit six prime factor integers that you can produce.


Q7)
Two members of a club are to be selected to represent the club at a national meeting.If there are 190 different possible selections of the 2 members,how many members does the club have?

There are 190 possible combinations of two members, order does not matter. There are initially n individuals to choose from, after the first person is picked then there are n-1 people to choose from.

n(n-1)/2 = 190
n(n-1) = 380
n = 20

Q8)
The figures given show sales for 5 salespeople.A-450000,B-360000,C-190000,D-210000,E-680000.It was discovered that one of C's sales was incorrectly recorded as A's.After this error was corrected,A's total sales were still higher than C's total sales and the median of the 5 sales totals was 330000.What is the value of incorrectly recorded sale?

The current median is 360000 (B's sales). Either salesperson A's sales drop by 120,000 or C's increased by 140,000. If Salesperson C's sales change by 140,000, he is now at 330,000 sales. salesperson A's sales will drop to 310,000. However, the problem states that "A's total sales are still higher than C's." Therefore, this scenario can be eliminated. If salesperson A drops from 450,000 to 330,000 then 330000 is the new median and A's sales are still higier than C's. Therefore, value of the incorrectly recorded sale must be 120,000.

Q9)
Working alone, at its own constant rate, a machine seals k cartons in 8 hours and working alone at its own constant rate, a second machine seals k cartons in 4 hours.If the two machines,each working at its own constant rate and for the same period of time together sealed a certain number of cartons,what percentage was sealed by the faster machine?

nothinglessthan780 wrote:Hi folks...I am not able to get the correct answer for the following questions on Gmatprep1..somebody please explain.

1.For all positive integers m,[m] = 3m when m is odd and [m]=1/2m when m is even.Which of the following is equivalent to [9]*[6]
A)81
B)54
C)36
D)27
E)18

Following the given info..i substituted m for 9 and since9 is odd [m] became 3*9 = 27 and m for 6 and since 6 is even it became (1/2)*6=3
therefore [9]*[6]=27*3=81 which is incorrect...
Anyone with an idea why D)27 is the correct answer?

2.Circular gears P and Q start rotating at the same time at constant speeds.Gear P makes 10 revolutions per minute and gear Q makes 40 revolutions per minute.How many seconds after the gears rotating will gear Q have made exactly 6 more revolutions than gear P?
No idea on how to solve this question.The correct given answer is 12.


Do explanations for GMATPrep Tests exist?