## Search found 1833 matches

#### It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike retur

###### Problem Solving

##### Re: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike r

$$Average=\frac{dis\tan ce}{time\ taken}$$ Distance between Mike's home and workplace=> $$=40\ miles\ per\ hour\ \cdot\ 1\frac{1}{2}=40\cdot1.5=60\ miles$$ Mike returns home along the same route at an average speed of 45 miles per hour. $$Time\ taken\ for\ return\ trip=\frac{dis\tan ce}{speed}=\frac...

- by deloitte247

Sun Jul 26, 2020 9:45 am- Forum: Problem Solving
- Topic: It takes Mike 1 hour and 30 minutes to commute from home to work at an average speed of 40 miles per hour. If Mike retur
- Replies:
**1** - Views:
**61**

#### If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction

###### Problem Solving

##### Re: If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fract

55% have brown hair, hence (100-55)% do not have brown hair. 80% do not have red hair, hence (100-80)% have red hair. Target question=>What fraction of those who do not have brown hair to those who have red hair. $$\frac{people\ with\ red\ hair}{people\ without\ brown\ hair}=\frac{100-80}{100-55}=\f...

- by deloitte247

Sun Jul 26, 2020 9:20 am- Forum: Problem Solving
- Topic: If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, what fraction
- Replies:
**2** - Views:
**67**

#### Given that \(N=a^3b^4c^5\) where \(a, b\) and \(c\) are distinct prime numbers, what is the smallest number with which

###### Problem Solving

##### Re: Given that \(N=a^3b^4c^5\) where \(a, b\) and \(c\) are distinct prime numbers, what is the smallest number with whi

The power exponents of a, b and c have to be divisible by 2, 3, and 5 for N to be a perfect square, perfect cube, and perfect 5th power. Therefore, we need to find the LCM of 2, 3, and 5. 2 = 1 * 2 3 = 1 * 3 5 = 1 * 5 LCM = 1 * 2 * 3 * 5 $$Therefore,\ the\ smallest\ integer\ N=a^{30}b^{30}c^{30}$$ $...

- by deloitte247

Sun Jul 26, 2020 2:52 am- Forum: Problem Solving
- Topic: Given that \(N=a^3b^4c^5\) where \(a, b\) and \(c\) are distinct prime numbers, what is the smallest number with which
- Replies:
**4** - Views:
**44**

#### A college admissions officer predicts that 20 percent of the students who are accepted will not attend the college.

###### Problem Solving

##### Re: A college admissions officer predicts that 20 percent of the students who are accepted will not attend the college.

20% of students who are accepted will not attend college. (100-20)% of students who are accepted will attend the college Let y = no of students that should be accepted to achieve a planned environment of x students. 80% of y = x $$\frac{80}{100}\cdot y=x$$ $$\frac{0.8y}{0.8}=x$$ $$y-\frac{x}{0.8}=1....

- by deloitte247

Sun Jul 26, 2020 2:27 am- Forum: Problem Solving
- Topic: A college admissions officer predicts that 20 percent of the students who are accepted will not attend the college.
- Replies:
**2** - Views:
**42**

#### On this year's Westchester basketball team, the players are all either \(5,7\) or \(11\) years of age. If the product of

###### Problem Solving

##### Re: On this year's Westchester basketball team, the players are all either \(5,7\) or \(11\) years of age. If the produc

Player's age is either 5, 7 or 11 years Product of ages of the players on the team is 18,865. Prime factors of 18865 = 5*7*7*7*11 There are 5 players and 3 of them are 7 years while the remaining 2 are not. Therefore, the probability that a randomly selected player will not be 7 = 2/5 Answer = optio...

- by deloitte247

Sun Jul 26, 2020 1:19 am- Forum: Problem Solving
- Topic: On this year's Westchester basketball team, the players are all either \(5,7\) or \(11\) years of age. If the product of
- Replies:
**1** - Views:
**43**

##### Re: The price of an automobile decreased m percent between 2010 and 2011 and then...

Let price in 2020 = y Price in 2011 = y * (1 - m/100) Price in 2012 = price in 2011 + (1 + n/100) $$=y\cdot\left(1-\frac{m}{100}\right)\cdot\left(1+\frac{n}{100}\right)$$ Target question=> Was the price of automobile lower in 2010 than in 2012? $$i.e\ y<y\cdot\left(1-\frac{m}{100}\right)\cdot\left(1...

- by deloitte247

Sat Jul 25, 2020 11:33 pm- Forum: Data Sufficiency
- Topic: The price of an automobile decreased m percent between 2010 and 2011 and then...
- Replies:
**2** - Views:
**110**

#### A rectangular solid box is \(x\) inches long, \(y\) inches wide, and \(z\) inches tall, where \(x, y,\) and \(z\) are

###### Data Sufficiency

##### Re: A rectangular solid box is \(x\) inches long, \(y\) inches wide, and \(z\) inches tall, where \(x, y,\) and \(z\) ar

Given that length = x inches, width = y inches and height = z inches. * Exactly tow of the length, width and height are equal, Target question: What is the total surface area? Surface area of a solid box = 2(h*w) + 2(h*l) + 2(w*l) Statement 1 => One face of the box has an area of 9 square inches. We...

- by deloitte247

Sat Jul 25, 2020 10:03 pm- Forum: Data Sufficiency
- Topic: A rectangular solid box is \(x\) inches long, \(y\) inches wide, and \(z\) inches tall, where \(x, y,\) and \(z\) are
- Replies:
**2** - Views:
**79**

#### If Angela is twice as old as the combined ages of Bill and Charlie, then how old is Charlie?

###### Data Sufficiency

##### Re: If Angela is twice as old as the combined ages of Bill and Charlie, then how old is Charlie?

... Let Bill's age = B, Charlie age = C, and Angela's = A. A = 2 (B+C) Target question => How old is charlie. A = 2B + 2C $$C=\frac{A-2B}{2}$$ Statement 1 => Four years now, the sum of all three people's ages will be 108. A+B+C+12 = 108 From question stem, A = 2 (B+C); A = 2B + 2C Therefore, 2B + 2C...

- by deloitte247

Sat Jul 25, 2020 2:35 pm- Forum: Data Sufficiency
- Topic: If Angela is twice as old as the combined ages of Bill and Charlie, then how old is Charlie?
- Replies:
**2** - Views:
**70**

##### Re: If \(2 + 5a - b/2 = 3c,\) what is the value of \(b?\)

$$2+5a-3c=\frac{b}{2}$$ $$b=2\left(2+5a-3c\right)$$ $$b=4+10a-6c$$ $$b=4+2\left(5a-3c\right)$$ Statement 1=> a + c = 13 a = 13 - c (substituting 'a' in the question stem expression), we have $$b=4+2\left[5\left(13-c\right)-3c\right]$$ $$b=4+2\left(65-5c-3c\right)$$ $$b=4+130-10c-6c$$ $$b=134-16c$$ H...

- by deloitte247

Sat Jul 25, 2020 1:08 pm- Forum: Data Sufficiency
- Topic: If \(2 + 5a - b/2 = 3c,\) what is the value of \(b?\)
- Replies:
**1** - Views:
**74**

#### In 2005, did Company \(A\) have more than twice the number of employees as did Company \(B?\)

###### Data Sufficiency

##### Re: In 2005, did Company \(A\) have more than twice the number of employees as did Company \(B?\)

i.e is A>2B in 2005? Statement 1=> In 2005, Company had 11,500 more employees than did Company A = B + 11,500. The exact value of A and B are unknown, so, we cannot estimate the value of A and B. Statement 2 => In 2005, the 3,000 employees with advanced degrees at Company made up 12.5 percent of tha...

- by deloitte247

Sat Jul 25, 2020 12:18 pm- Forum: Data Sufficiency
- Topic: In 2005, did Company \(A\) have more than twice the number of employees as did Company \(B?\)
- Replies:
**1** - Views:
**73**

#### A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of...

###### Problem Solving

##### Re: A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of...

Let the number of coffee cups sold = c Let the number of the newspaper sold = n Let the number of gums sold = g Compared to cups of coffee, he sells twice as many packs of gum and three times as many newspapers g = 2c and n = 3c Price of c = $1.25 Price of n = $0.50 Price of g = $0.35 Total gross sa...

- by deloitte247

Sun Jul 19, 2020 8:17 am- Forum: Problem Solving
- Topic: A magazine stand owner sells cups of coffee, newspapers, and packs of gum. Compared to the number of cups of...
- Replies:
**2** - Views:
**241**

#### Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park...

###### Data Sufficiency

##### Re: Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park...

Let adult ticket = a; child ticket = c; and senior ticket = s a = 2, c = 1, s = 1 Total ticket = 4 Discount on a = 30% of a's price Discount on c = 15% on c's price Discount on s = 15% on s' price Target question => Was the total amount of the 4 discounts greater than 20% of the sum of the regular ...

- by deloitte247

Sun Jul 19, 2020 7:04 am- Forum: Data Sufficiency
- Topic: Julie bought 2 adult tickets, 1 child ticket, and 1 senior ticket to an amusement park...
- Replies:
**1** - Views:
**123**

##### Re: At a certain clothing store, customers who buy 2 shirts pay the regular price

Customers who buy 2 shirts pay the regular price for the first shirt and a discounted price for the second shirt Profit made in selling either 1 or 2 shirts is the same. This means that the discounted shirt is sold with no profit at all hence discounted price of the second shirt = cost price of each...

- by deloitte247

Sat Jul 18, 2020 1:30 pm- Forum: Data Sufficiency
- Topic: At a certain clothing store, customers who buy 2 shirts pay the regular price
- Replies:
**2** - Views:
**150**

##### Re: A telephone station has x processors, each of which can process a maximum

Target question => If 500 calls are sent to the station at a particular time, can the station process all of the calls? The station has x processors and each of x can process a maximum of y calls at a particular time So from target question, we want to estimate if xy > 500; where x > = 1 and y > = ...

- by deloitte247

Sat Jul 18, 2020 12:53 pm- Forum: Data Sufficiency
- Topic: A telephone station has x processors, each of which can process a maximum
- Replies:
**2** - Views:
**127**

#### In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6

###### Problem Solving

##### Re: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 t

Distributing 6 identical chocolates among 3 children using permutation and combination to find the whole solution (n + r - 1) C(r - 1) This will give the number of ways n identical chocolates can be distributed for r different children Given that; n = 6 and r = 3 (n + r - 1) C( r - 1) (6 + 3 - 1) C(...

- by deloitte247

Sat Jul 18, 2020 12:05 pm- Forum: Problem Solving
- Topic: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 0 to 6
- Replies:
**1** - Views:
**111**