Problem Solving

c210 wrote:Hey Guys and Gals,

everyone was really helpful when i first posted some questions regarding gmat prep q's and I really appreciate it. Here are some more, I hope you can take the time to help me figure it out!

1. If ax+b=0 is X>0?

1) A+b>0
2) A-b >0

I got this problem wrong, but the main issue is,what is the quickest easiest way to solve these type of problems? and whats the solution for this one
(answer E)
x = -b/a, It will be positive if a and b are of opposite signs. Both the statements do not lead to a definite answer if a nd b are of oppiosite signs, hence (E)

2. The number X and Y are not integers. the value of X is closest to which integer?

1) 4 is the integer closets to X + Y
2) 1 is the integer closest to X-Y

I have the same issue with this problem as I don't know the best way to approach it.

IMO (C) is the answer.

3. The sum of the first 50 positive integers is 2,550. What its he some of the even integers from 102-200 inclusive?

answer is 7550, and i have no idea how they came about it.

Treat it as sum of AP with first term last term and no of terms known to you.

4. A certain circular area has its center at point P and radius 4, and the points X and Y lie int eh same plane as the circular area. Does point Y lie outside the circular area?

1) the distance between point P and point X is 4.5
2) the distance between point X and Y is 9

answer is C but why is it not A? couldn't you solve it already know that the X coordinate is outside of the radius?

The first statement clearly tells you that X is outside the circle, but nothing can be said of Y. Hence (C)

5. if mv<pv<0 is V>0?
1)m<P
2)m<0

answer is D, why? how does M<p solve it? when you take into account M<p are you also taking into account that both are <0 ?
I think (B) should be the answer as mv<0 and m<0 implies v>0

6. if x<0 then Sqrt(-x|x|) is? answer is -x...but shouldn't it be positive x?
Since sqrt (X^2) = |X|, sqrt (-x|x|) = -x as x<0

7. if an equilateral triangle with side T and square with sides s had the same area, what is the ratio of T: S?
Area triangle = sqrt (3)* (Side)^2/4

answer is 2: 3^1/4

no idea why

8. At the bakery lew spent a total of 6$ for one kind of cupcake and one kind of doughnut. How many donuts did he buy?
1) price of 2 doughty was $.10 less than 3 cupcakes
2) average price of 1 doughnut and 1 cupcake was $.035

answer is E, but couldn't you solve it with C ( since 2 equations and 2 unknowns are produced? )
We can only get prices of doughnuts and cupcakes not there quantities.

9. A certain list consists of several different integers. is the product of all the integers in the list positive?

1) the product of the greatest and smaller of the integers in the list is positive
2) there is an even number of integers in the list

answer is C, wheres the logic in this?

Did not get the question. Sorry

and FINALLY

10) 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 then F(p) =?

It will be p-1 as prime number will not have any common factor which need not be counted in the definition of the function.

a) p-1
b) p-2
c) (p+1)/2
d (p-1)/2
E) 2

i got the answer A correctly but was guessing, whats the smartest way to solve this problem and these kinds of problems?

thank you all so very much! i really appreciate the help!

best,

c

Anurag@Gurome wrote:

3. The sum of the first 50 positive integers is 2,550. What its he some of the even integers from 102-200 inclusive?

answer is 7550, and i have no idea how they came about it.

We have to find 102 + 104 + 106 +....+ 200 = (100 + 2) + (100 + 4) + (100 + 6) +....+ (100 + 100)
= (100 + 100 + 100 +...+ 100) + (2 + 4 + 6 +...+ 100)

It is given that 2 + 4 + 6 + .... + 100 = 2,550

Now 100 will occur 50 times, so the above sum can be written = (50 X 100) + 2,550 = 5,000 + 2,550 = 7,550

So, the correct answer is 7,550.

Anurag@Gurome wrote:

10) 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 then F(p) =?

a) p-1
b) p-2
c) (p+1)/2
d (p-1)/2
E) 2

i got the answer A correctly but was guessing, whats the smartest way to solve this problem and these kinds of problems?

thank you all so very much! i really appreciate the help!

Tricky solution:

Let us take p = 2 (smallest prime)
Now number of positive integers less than p and has no common factor with p other than 1 is 1. So f(2) = 1

Only option A satisfies this result.

Mathematical Approach:

Note that a prime number will have common factors other than 1 only with its multiples like p², p³ etc. As p is always greater than 1, all multiples of p are greater than p. Hence, none of the integers less than p will have any common factor with p.

Thus, f(p) = Number of positive integers less than p = (p - 1)

The correct answer is A.