## Search found 15 matches

#### A loan of $10,000 has an annual interest rate of 8%, compounded quarterly. What will be the total due (principal + inter

###### Problem Solving

##### Re: A loan of $10,000 has an annual interest rate of 8%, compounded quarterly. What will be the total due (principal + i

Since, annual interest is \(8\%\) , interest per quarter is \(2\%\)

Number of payment periods = Number of quarters in 12 months = 4

Amount due = $$P\ \cdot\ \left(1.02\right)^4\ =\ 10000\ \cdot\ \left(1.0824\right)\ =\ 10824$$ D

- by orthodoxparadox

Sat May 30, 2020 11:59 pm- Forum: Problem Solving
- Topic: A loan of $10,000 has an annual interest rate of 8%, compounded quarterly. What will be the total due (principal + inter
- Replies:
**1** - Views:
**193**

#### Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take

###### Problem Solving

##### Re: Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take

Let percentages be as follows \(a\%\) - Physics \(b\%\) - Calculus \(c\%\) - Both \(d\%\) - None Clearly, $$a\ +\ b\ +\ c\ +\ d\ =\ 100$$ $$a\ +\ c\ =\ 40$$ $$\left(b\ +\ d\right)\ =\ 100\ -\ \left(a\ +\ c\right)\ =\ 60$$ $$20\%\ \cdot\ \left(b\ +\ d\right)\ =\ b\ \ =12\%$$ $$d\ =\ 100\ -\ a\ -\ b\ ...

- by orthodoxparadox

Sat May 30, 2020 11:56 pm- Forum: Problem Solving
- Topic: Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take
- Replies:
**1** - Views:
**198**

#### Coins are dropped into a toll box so that the box is being filled at the rate of approximately 2 cubic feet per hour. If

###### Problem Solving

##### Re: Coins are dropped into a toll box so that the box is being filled at the rate of approximately 2 cubic feet per hour

Let the volume of the cube be \(V\)

Let the rate of filling it be \(r\)

So, time taken to fill the box will be \(\frac{V}{r}\)

$$V\ =\ 4\ \cdot\ 4\ \cdot\ 3\ =\ 48$$ $$r\ =\ 2$$ $$\frac{V}{r}\ =\ \frac{48}{2}\ =\ 24$$ D

- by orthodoxparadox

Sat May 30, 2020 11:48 pm- Forum: Problem Solving
- Topic: Coins are dropped into a toll box so that the box is being filled at the rate of approximately 2 cubic feet per hour. If
- Replies:
**1** - Views:
**198**

#### From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the

###### Problem Solving

##### Re: From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the

Let ways of choosing a white marble and a red marble be w Let total ways of choosing 2 marbles be W So, the Probability of choosing a white a red marble = \(\frac{w}{W}\) w = \(\left(4\ choose\ 1\right)\ \cdot\ \left(2\ choose\ 1\right)\) = 8 W = \(\left(6\ choose\ 2\right)\) = 15 So answer is \(\fr...

- by orthodoxparadox

Sat May 30, 2020 11:45 pm- Forum: Problem Solving
- Topic: From a jar containing 4 red and 2 white marbles, Lionel draws two marbles simultaneously and at random. What is the
- Replies:
**1** - Views:
**199**

#### If 1,500 is increased by 20% and then reduced by \(y\%,\) yielding 1,080, what is \(y ?\)

###### Problem Solving

##### Re: If 1,500 is increased by 20% and then reduced by \(y\%,\) yielding 1,080, what is \(y ?\)

When 1500 is increased by 20% it becomes \(\frac{120}{100}\ \cdot\ 1500\ =\ 1800\) Now when 1800 is decreased by y% it becomes 1080. So $$\frac{\left(100\ -\ y\right)}{100}\ \cdot\ 1800\ =\ 1080$$ \(\left(100\ -\ y\right)\ \cdot\ 18\ =\ 1080\) $$\left(100\ -\ y\right)=\ \frac{1080}{18}\ =\ 60$$ $$y\...

- by orthodoxparadox

Sat May 30, 2020 11:41 pm- Forum: Problem Solving
- Topic: If 1,500 is increased by 20% and then reduced by \(y\%,\) yielding 1,080, what is \(y ?\)
- Replies:
**1** - Views:
**215**

#### Nicky and Chadi begin running a race at the same time, though Nicky starts the race 36 meters ahead of Chadi. If Chadi

###### Problem Solving

##### Re: Nicky and Chadi begin running a race at the same time, though Nicky starts the race 36 meters ahead of Chadi. If Cha

Speed of Chadi = 5m/s

Speed of Nicky = 3m/s

Speed by which Chadi catches up with Nicky = 5m/s - 3m/s = 2m/s

Distance that Nicky is initially ahead = 36m

So time taken to catch up = \(\frac{36}{2}\ =\ 18\) B

- by orthodoxparadox

Sat May 30, 2020 11:37 pm- Forum: Problem Solving
- Topic: Nicky and Chadi begin running a race at the same time, though Nicky starts the race 36 meters ahead of Chadi. If Chadi
- Replies:
**1** - Views:
**204**

#### Cost is expressed by the formula \(tb^4.\) If \(b\) is doubled and \(t\) remains the same, the new cost is how many time

###### Problem Solving

##### Re: Cost is expressed by the formula \(tb^4.\) If \(b\) is doubled and \(t\) remains the same, the new cost is how many

Let \(t'\) and \(b'\) be the new parameters.

So,

\(t'\ =\ t\) and \(b'\ =\ 2\ \cdot\ b\)

New cost = \(t'\ \cdot\ b'^4\ =\ t\cdot\left(2\cdot b\right)^4\ =\ t\cdot16\cdot b^4\ =\ 16tb^4\)

So, the answer is 16 E

- by orthodoxparadox

Sat May 30, 2020 11:35 pm- Forum: Problem Solving
- Topic: Cost is expressed by the formula \(tb^4.\) If \(b\) is doubled and \(t\) remains the same, the new cost is how many time
- Replies:
**1** - Views:
**205**

#### A 400 milliliter solution is 20% alcohol by volume. If 100 milliliters of water is added, what is the new concentration

###### Problem Solving

##### Re: A 400 milliliter solution is 20% alcohol by volume. If 100 milliliters of water is added, what is the new concentrat

Initially, the solution is \(20\%\) alcohol by volume. This means that out of 400 ml of the solution, Volume of alcohol = $$\frac{20}{100}\ \cdot\ 400\ =\ 80$$ Since, we add 100ml water to this solution, the volume of solution becomes 500ml, but the volume of alcohol does not change. So, now the con...

- by orthodoxparadox

Sat May 30, 2020 11:31 pm- Forum: Problem Solving
- Topic: A 400 milliliter solution is 20% alcohol by volume. If 100 milliliters of water is added, what is the new concentration
- Replies:
**1** - Views:
**189**

#### The average (arithmetic mean) of 11 numbers is 10. When one number is eliminated, the average of the remaining numbers

###### Problem Solving

##### Re: The average (arithmetic mean) of 11 numbers is 10. When one number is eliminated, the average of the remaining numbe

We know that if mean of \(n\) numbers is \(M\) , then sum of the numbers is \(n\ \cdot\ M\)

So, sum of the 11 numbers is \(11\ \cdot\ 10\ =\ 110\)

After removing one number, sum of remaining numbers is \(9.3\ \cdot\ 10\ =\ 93\)

So the removed number is \(110\ -\ 93\ =\ 17\) D

- by orthodoxparadox

Sat May 30, 2020 11:28 pm- Forum: Problem Solving
- Topic: The average (arithmetic mean) of 11 numbers is 10. When one number is eliminated, the average of the remaining numbers
- Replies:
**1** - Views:
**218**

#### An empty bucket is filled with paint at a constant rate, and after 6 minutes the bucket is filled to 3/10 of its

###### Problem Solving

##### Re: An empty bucket is filled with paint at a constant rate, and after 6 minutes the bucket is filled to 3/10 of its

Since, $$\frac{3}{10}$$ of the bucket took 6 minutes to fill.

Therefore, total time to fill the bucket is $$\frac{1}{\frac{3}{10}}\cdot\ 6\ =\ \frac{10}{3}\ \cdot\ 6\ =\ 20$$ minutes.

So remaining time to fill the bucket = $$20\ -\ 6\ =\ 14$$

- by orthodoxparadox

Sat May 30, 2020 11:25 pm- Forum: Problem Solving
- Topic: An empty bucket is filled with paint at a constant rate, and after 6 minutes the bucket is filled to 3/10 of its
- Replies:
**1** - Views:
**195**

#### The price of a model \(M\) camera is $209 and the price of a special lens is $69. When the camera and lens are purchased

###### Problem Solving

##### Re: The price of a model \(M\) camera is $209 and the price of a special lens is $69. When the camera and lens are purch

Cost of Camera = $$209$$

Cost of Lens = $$69$$

Sum of Costs = $$209\ +\ 69\ =\ 278$$

Retail price = $$239$$

Money Saved = $$278\ -\ 239\ =\ 39$$

Therefore, money saved as percent of total amount = $$\frac{39}{278}\cdot100=\ \sim14\%$$

- by orthodoxparadox

Sat May 30, 2020 11:23 pm- Forum: Problem Solving
- Topic: The price of a model \(M\) camera is $209 and the price of a special lens is $69. When the camera and lens are purchased
- Replies:
**1** - Views:
**184**

#### In the coordinate plane, one of the vertices of a square is the point \((-3, -4).\) If the diagonals of that square

###### Problem Solving

##### Re: In the coordinate plane, one of the vertices of a square is the point \((-3, -4).\) If the diagonals of that square

Let the length of the side of the square be s. Note that diagonals of a square intersect at the center of the square. Therefore, by Pythagoras theorem (s/2) $$\left(\frac{s}{2}\right)^2\ +\ \left(\frac{s}{2}\right)^2$$ = square of distance between vertex and center. So $$\left(\frac{s}{2}\right)^2\ ...

- by orthodoxparadox

Sat May 30, 2020 11:16 pm- Forum: Problem Solving
- Topic: In the coordinate plane, one of the vertices of a square is the point \((-3, -4).\) If the diagonals of that square
- Replies:
**1** - Views:
**179**

#### When positive integer \(n\) is divided by 13, the remainder is 2. When \(n\) is divided by 8, the remainder is 5. How

###### Problem Solving

##### Re: When positive integer \(n\) is divided by 13, the remainder is 2. When \(n\) is divided by 8, the remainder is 5. Ho

Since there are not many values that give remainder 2 with 13 under 180, we can evaluate them individually.

15 -> 7

28 -> 4

41 -> 1

54 -> 6

67 -> 3

80 -> 0

93 -> 5

106 -> 2

119 -> 7

132 -> 4

145 -> 1

158 -> 6

171 -> 3

Hence there is only 1 value (93) B

- by orthodoxparadox

Sat May 30, 2020 11:11 pm- Forum: Problem Solving
- Topic: When positive integer \(n\) is divided by 13, the remainder is 2. When \(n\) is divided by 8, the remainder is 5. How
- Replies:
**1** - Views:
**207**

##### Re: If x is an integer greater than 2, the function f(x)

Let us evaluate f(51) in terms of f(50).

Since f(51) = 2 * 4 * 6 * ... * 50

And f(50) = 2 * 4 * 6 * ... * 50

Therefore f(51) = f(50)

So f(51) - f(50) = f(50) - f(50) = 0 (E)

- by orthodoxparadox

Sat May 30, 2020 11:04 pm- Forum: GMAT Math
- Topic: If x is an integer greater than 2, the function f(x)
- Replies:
**5** - Views:
**6319**

##### Re: Quant- Numbers Problem

Let us try it for all n from -20 to 20. We can only choose such n that 20 - n is divisible by 4, since m is also an integer. Since 20 is divisible by 4, n must also be divisible by 4.

So values would be -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20 => 11 values in total.

- by orthodoxparadox

Sat May 30, 2020 10:57 pm- Forum: GMAT Math
- Topic: Quant- Numbers Problem
- Replies:
**2** - Views:
**4547**