Problem Solving

Hello everyone,

I took a test from the Gmatprep software and got the following questions wrong. Since the prep doesnt give explanations i need help with understanding these questions. The answers are given below but i dont know how to arrive at them. Can someone pls help?

1) If each term in the sum a1 + a2 +....an is either 7 or 77 and the sum equals 350, which of the following is n

38
39
40
41
42

Ans - 40



2) Pumps A, B, C operate at their respective rates. Pumps A & B operating simultaneously can fill a certain tank in 3/2 hours. Pumps B & C operating simultaneously can fill a certain tank in 2 hours. How many hours does it take pumps A, B, C to fill the tank.

1/3
1/2
2/3
5/6
1

Ans - 1 hour


3) For every positive even integer n, the function h(n) is defined to be the product of even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is

between 2 and 10
between 10 and 20
between 20 and 30
between 30 and 40
greater than 40

Ans - greater than 40



4) In the xy plane at what two points does the graph of y = (x+a) (x+b) intersect the x-axis

i) a + b = -1

ii) the graph intersects at y-axis at 0,-6

Ans - C (both statements are necessary)

1) If each term in the sum a1 + a2 +....an is either 7 or 77 and the sum equals 350, which of the following is n

38
39
40
41
42

Ans:

Total number of terms = n
Say total number of 77 in the sequence are = x
Then total number of 7 in the seq are = n-x

Thus we can write: 77x + 7(n-x) = 350
=> 11x+n-x = 50
=> 10x+n = 50

Now go to the options and tell me which one if u plug the value as n to the equation 10x+n = 50 then you will get a proper x (I mean Integer).

Thus Ans is 40.

Substitution is the best or I can say Only way to solve here.

2) Pumps A, B, C operate at their respective rates. Pumps A & B operating simultaneously can fill a certain tank in 3/2 hours. Pumps B & C operating simultaneously can fill a certain tank in 2 hours. How many hours does it take pumps A, B, C to fill the tank.

1/3
1/2
2/3
5/6
1

I strongly believe u missed some part. We have 2 eqn here and 3 variabls not possible to solve. Information about A and C operating together is missing it seems.

4) In the xy plane at what two points does the graph of y = (x+a) (x+b) intersect the x-axis

i) a + b = -1

ii) the graph intersects at y-axis at 0,-6

Ans:
What is asked?
In the xy plane at what two points does the graph of y = (x+a) (x+b) intersect the x-axis.
We can simplify it to 0 = (x+a) (x+b) [intersect at X-axis means y=0]
so x = -a or -b

So basically it asks us what is a and b?

1. a+b = -1. a and b can be anything -3 and 2; -4 and 3.
So we cannot say any concrete valus of a and b. So not Sufficient .

2. y intercept is -6
But before that let us simplify the eqn:
y = (x+a) (x+b)
=> y = x^2+(a+b)x+ab

Now plug the point (0,-6) to the above eqn:
-6 = 0 + (a+b) 0 + ab
=> ab=-6

But we cannot say what is the value of a or b. So not Suff.

Combine 1 and 2:
a+b = -1
ab = -6

Two equations two variables. So sufficient.

Many Thanks Shovan for the prompt reply

sorry for typing the wrong question. the correct part of the qn is as under:

pump A&B - 6/5 hrs
pump B&C - 3/2 hrs
pump A&C - 2 hrs

Rupal Gori wrote:sorry for typing the wrong question. the correct part of the qn is as under:

pump A&B - 6/5 hrs
pump B&C - 3/2 hrs
pump A&C - 2 hrs

When the job is undefined, we can plug in. Let tank = 18.

Rate for A+B = w/t = 18/(6/5) = 15.
Rate for B+C = w/t = 18/(3/2) = 12.
Rate for A+C = w/t = 18/2 = 9.

Combining the rates above, we get:
(A+B) + (B+C) + (A+C) = 15+12+9
2A + 2B + 2C = 36
A+B+C = 18

So time for A+B+C = w/r = 18/18 = 1.