Quantitative Practice Questions - 2

The solution he needs has only a 10% salt level. Currently we know that his solution has 20 ounces at 25% salt. We can calculate the amount of salt in the 20 ounce container by utilizing the given information. (20) * (.25) = 5 ounces of salt. Let x be the volume of pure water (in ounces) added. 

Therefore, we know the total volume of our new solution will be 20 + x.  We know we want our solution to have 10% salt, so our salt amount in the new solution will have to be (20+x)  * (.10). Since we are not adding any salt when we add our "pure water", we know the total salt in the solution will not change. Therefore, we can write the equation. (20+x) * (.10) = 5

Solve for x and you get x = 30 ounces of pure water. 

To calculate simple interest, the formula is

  FV = PV(1 + it) 

where  FV  stands for Future Value,  PV  stands for Present Value,  i  stands for the interest rate, and  t  stands for the number of periods (in this case years). So plugging in, 

15,000 = 10,000(1+10i) = 10,000 + 100,000i 

Solving this we get  i =. 05 

or 5%

ALTERNATE SOLUTION:

Another way of finding this is to calculate the amount of interest per year. Since this is simple interest, Grandpa Jack earns the same amount of interest per year. The total interest earned is 15,000 - 10,000 = 5,000. $5,000 over 10 years, equates to $500 per year. $500 divided by the original $10,000 is .05, or 5%.

Let  x  equal the original price.

First discount:  x(1 − 0.20) = 0.80x  (sale price).

Second discount:  0.80x(1 − 0.25) = 0.60x  (final sale price)

Therefore, the final price is 60% of the original price. To calculate the discount:

1 − 0.60 = 0.40  or 40%

There are 36 possible outcomes ( 6 × 6=  36 ). 10 out of the 36 outcomes are greater than 8: (6 and 3)(6 and 4)(6 and 5)(6 and 6)(5 and 4)(5 and 5)(5 and 6)(4 and 5)(4 and 6)(3 and 6).

10/36 = 5/18

Of the  100  people,  76   (36 + 16 + 24)  were either men or blonde or both. Therefore,  24  are non-blonde and non-men (women).

100 − 76 = 24

We can calculate the two individual probabilities first.

Prob(die shows even) = 3 / 6 = 1/ 2 (2, 4, and 6 out of 1, 2, 3, 4, 5, and 6)

Prob(tail) = 1/2 (tail out of head and tail)

Then, Prob(even AND tail) is 

= 1/4

To find the average, multiply each expected profit or loss by its probability:

27 is a little less than 29, which is 10% of $290. Therefore, 9% is the closest approximation. 

The formula to find the average speed is  avg. speed = total distance / total time .

Since the question deals with miles per hour, the time must be converted to hours from minutes:

75 min / 60 min = 1.25 hours 

Plugging the numbers into the equation gives  50 miles / 1.25 hours = 40 mph .

Let  x  be the number of minutes that it takes to drain the tank.

Think of emptying the tank as one job. Then the drain can do one job in 25 minutes, or  1 / 25  jobs per minute.

Now, think of the inlet pipe as doing a "negative" job - it is doing the opposite of emptying the tank, working against the drain. It is doing "negative one" job in 45 minutes, or  −1 / 45  jobs per minute.

Now, think of this as a rate problem. In  x  minutes, the drain does 

1 / 25x  jobs

and the pipe does

−1 / 45x  jobs.

Together they do 1 job, the draining of the whole tank. 

Set up an equation to solve for x:

x = 56.25 , which rounds to 56 minutes.

1,728 ÷ 3 = 576 , making 1,728 a multiple of 3, and thus, an element of A.

1,728 is not a perfect square; 41² = 1,681 < 1,728 < 1,764 = 42². Thus, 1,728 is not an element of B.

1,728 is a perfect cube: 1,728 = 12³. Thus, 1,728 is an element of C.

, which is represented by the region inside circles A and C and outside B. This is region IV.

A = p + prt  

A = accumulated sum; p = principle; r = rate; t = time in years

A = 5000 + 5000(0.06)5 = 6500

We need to convert hours into minutes and multiply this by the 10 minute time interval:

= 2 miles

The length of the track equals the circumference of the circle.

C = 2πr 

C = 2π(200) = 400π

Speed = Distance / Time

Therefore, Time = Distance /  Speed

= 800 seconds

Explanation:
The easiest way to solve this is by using the complement. Only one of the five plates is NOT blue or green. So 1/5  of the plates are NOT blue or green.  Therefore1 - 1/5  = 4 / 5 of the plates are blue or green.

One of the easiest way would be to equate time..

In 12 minutes, S covers = 12/60*50=10 miles..

Let the two catch up at x miles in third stretch
1) S covers 20 miles at 50mph, then 10 and 40mph and say x at 50mph ----- Time taken 
2) F covers 30 miles at 60mph, then 10 and 40mph and x at 55mph ----- Time taken 
Both should be equal.. 
So, ----- Time taken 

So they meet when they have covered 55 miles in last 60 miles. Hence 5 miles short of final destination.

Since 'm' and 'n' are 2-Placer , product m∗n can be rewritten as  and n/100 = N
In Order for product M*N/10000 to be 2-Placer there should be 2 '0' in product of M*N so , there should be 2*2*5*5 i.e. 100 in M*N .
Also , note that neither M nor N will be a multiple of 10 so M will be a multiple of 4 (without 5) and N will be a multiple of 25.
Possible values of 
Possible values of N = 25, 75 = 2 Values

Answer 2*20 = 40 = A

numbers are a,b,b,b,100+a
2a+3b+100=150*5=750
, note that 'b' has to be an even integer in order to get a an integer value
we know b > a

we know that b<100+a

130<b<170
and since b is even , we will get only 19 such values.
Answer 19.

To find the probability of selecting a matched set of gloves, the following calculations are performed:

1. Total Number of Ways to Select Three Gloves:

   There are 10 gloves in total: 6 blue (3 left, 3 right) and 4 green (2 left, 2 right). The total number of ways to select three gloves is calculated using the combination formula:

   C(10, 3) = 10! / [3! × (10 - 3)!]
   = (10 × 9 × 8) / (3 × 2 × 1)
   = 120

   Total ways to select three gloves: 120

2. Favorable Outcomes:

   We calculate the number of outcomes where at least one pair of gloves is complete. Two main cases are considered:

   Case 1: Selecting one complete pair (either blue or green) and one glove of a different color:

   • Ways to select a blue pair = C(3, 2) = 3
   • Ways to select a green pair = C(2, 2) = 1
   • Ways to select one glove from the remaining gloves = C(8, 1) = 8
   • Total outcomes for this case: (3 + 1) × 8 = 32

   Case 2: Selecting two gloves of one color and one glove of another color, ensuring at least one pair is complete:

   • Ways to select two blue gloves and one green glove = C(3, 2) × C(2, 1) = 3 × 2 = 6
   • Ways to select two green gloves and one blue glove = C(2, 2) × C(3, 1) = 1 × 3 = 3
   • Total outcomes for this case: 6 + 3 = 9

   Total Favorable Outcomes:
   Total for both cases = 32 + 9 = 104

3. Probability Calculation:

   The probability of selecting a matched set of gloves is:

   P = Favorable Outcomes / Total Outcomes
   P = 104 / 120

   Simplify the fraction:
   P = 52 / 60

4. Final Answer:
   The probability of selecting a matched set is 52/60.

4o

First let's find the max these can be
Say cars with camera is C..
So 18% of C have both C & S...
Now 120 of 4-door cars have C..
Say all 2-door cars have C, that is 165..
So C has to be lesser than or equal to 120+165 or 285
What is the number of 4-door cars with C&S
60% of 18% of C or 

But 0.108*C has to be an integer
There are three DECIMALS, so it has to multiplied with 3 TENS or 3*2s and 3*5s..
108 is a multiple of 4 so 2*2s are already there so C has to be multiple of (3-2)*2s and 3*5s..
That is 2*5*5*5=250.. so 250 or 250*2=500
Also C cannot be MORE than 285, so ONLY possible value is 250..

Now 0.108*C= 0.108*250 = 27

Actual price = 120
Payment with interest = 20+12*10 = 140
Interest = 140-120 = 20
% of interest of the purchase price = 20/120 = 1/6 = 16.67%