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: 2
- Views: 469
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: 398
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: 408
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: 427
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: 460
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: 434
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: 427
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: 406
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: 459
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: 393
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: 381
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: 389
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: 400
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: 13117
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: 3
- Views: 14833