Search found 1833 matches


Re: Solution \(X,\) which is \(10\%\) alcohol is combined with solution \(Y,\) which is \(18\%\) alcohol to form a new s

Concentration of X = 10% Concentration of Y = 18% Concentration of X + Y= 12% Target question: How many liters of solution Y are in the new combined solution? Using allegation rule to find the ratio of mixing the solutions. $$\frac{Value\ of\ X}{Value\ of\ Y}=\frac{\left(Conc.\ of\ Y\right)-\left(Co...


Re: An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the s

The ratio of cats to dogs = 5:11 Target question=> What was the ratio of cats to dogs at the end of the day Tuesday? Statement 1: No cats were adopted on Tuesday No information was provided on the number of adopted dogs. Hence, the target question cannot be answered. Thus, statement 1 is NOT SUFFICI...


Re: The sequence \(a_1, a_2, \ldots, a_n,\ldots\) is such that \(a_n=\sqrt{a_{n-1}\cdot a_{n-3}}\) for all integers

$$Given\ that\ a_n=\sqrt{\left(a_{n-1}\right)\cdot\left(a_{n-3}\right)}\ \ when\ n\ge4$$ $$a_4=\sqrt{\left(a_{4-1}\right)\cdot\left(a_{4-3}\right)}\ \ =\sqrt{a_3\cdot a_1}=16$$ Target question=> What is the value of $$a_6=\sqrt{\left(a_{6-1}\right)\cdot\left(a_{6-3}\right)}\ \ =\sqrt{a_5\cdot a_3}$$...


Re: The first and second numbers in a sequence of numbers are plotted as the \(x\) and \(y\) coordinates, respectively,

Let the first number = x, then we have (x, x+1) coordinate, (x+2, x+3) coordinates. Target question=> A line is formed by connecting the coordinate, what would be the slope of the line? $$Slope=\frac{\triangle y}{\triangle x}=\frac{y2-y1}{x2-x1}$$ Statement 1: Except for the first number, the sequen...


Re: The probability of rain on each of five days is 1/6, except on the first day when it is 2/5, and on the last day, wh

Probability of rain on the first day = 2/5 Probability of rain on the last day = 4/5 Probability of rain on other days = 1/6 $$\Pr obability\ of\ not\ raining\ on\ first\ day=1-\frac{2}{5}=\frac{3}{5}$$ $$\Pr obability\ of\ not\ raining\ on\ last\ day=1-\frac{4}{5}=\frac{1}{5}$$ $$\Pr obability\ of\...


Re: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank th

Total contestants = 7 Finalist needed = 5 Highest rank = 3 Judges will select 5 out of 7 contestants and how to select 3 top ratings from the 5. $$7C_5\cdot5C_3$$ $$7C_5=\frac{7!}{5!\left(7-5\right)!}=\frac{7\cdot6\cdot5!}{5!\cdot2\cdot1}=\frac{42}{2}=21$$ and $$5C_3=\frac{5!}{3!\left(5-3\right)!}=\...


Re: What is the average (arithmetic mean) of x and y?

$$Mean=\frac{E\ Fx\ }{Ef}=\frac{x+y}{2}$$ Target question: What is the mean of x and y? Statement 1: The average (arithmetic mean) of x, y, and k is 7. $$\frac{x+y+k}{3}=7$$ $$x+y+k=21$$ The value of x and y remains unknown; so, therefore, we cannot the target question at this point. Statement 2: Th...

by deloitte247

Fri Jul 31, 2020 7:53 am
Forum: Data Sufficiency
Topic: What is the average (arithmetic mean) of x and y?
Replies: 1
Views: 45

Re: An insurance company sells only one type of health and one type

Let the no. of insurance policy = x Let the no. of life policy = y Let the no. of a monthly premium of a life insurance policy = z Let the no. of a monthly premium of a health insurance policy = $80 Target question: What was the monthly premium of a life insurance policy? Given that 80x + zy = 5000;...


Re: Percents and Interest Problems, Word Problems

Let the certain investment = x
x earns 20% annually to give $30
Therefore, 20% of x = 30
$$\frac{20}{100}\cdot x=30$$
$$x=\frac{30\cdot100}{20}=$150$$

Answer = option C

by deloitte247

Fri Jul 31, 2020 12:51 am
Forum: Problem Solving
Topic: Percents and Interest Problems, Word Problems
Replies: 2
Views: 56

Re: Word Problems

Let Rob's age now = r
Let Jodie's age now = j
r = 2j ----- eqn (1)
In 10 years time =>
r + 10 = (j + 10) + 20
r + 10 = j + 30
r = j + 20 where r = 2j
2j = j + 20
j = 20 years

Answer = option B

by deloitte247

Thu Jul 30, 2020 11:22 pm
Forum: Problem Solving
Topic: Word Problems
Replies: 2
Views: 46

Re: Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than

Jane started babysitting when she was 18 years old.
$$The\ child\ at\ that\ time\ was\ 18\cdot\frac{1}{2}=9\ years\ old$$
The difference in years between when James started and now = 32 - 18 = 14 years.
The child's current age = 9 + 14 = 23 years old
Answer = option C


Re: Bob leaves point \(A\) and drives due west to point \(B.\) From point \(B,\) he drives due south to point \(C.\) How

.Bob leaves point A and drives due west to point B. From point B, Bob drives due south to point C. Target question => How far is Bob from his original position. Plotting the bearing of Bob's journey gives a right-angle triangle in which AB = base, BC = height, and CA = hypotenuse. Find CA = hypotenu...


Re: The height of a certain right circular cylinder is greater than its diameter, and both numbers are positive integers

Given that height > Diameter Target Question=> What is the volume of the cylinder? $$volume\ =\pi r^2h$$ Therefore, height >2r because d=2r Statement 1=> The radius of the base is 2.5. Height is unknown, so, the target question cannot be evaluated. Statement 1 is NOT SUFFICIENT. Statement 2=> The lo...


Re: David has 3 credit cards: a Passport card, an EverywhereCard, and an American local card. He owes a balance on all t

let passport card = p ; everywhere card = e , and American card = a Target question= Does he get owe the greatest balance on everywhere card. $$i.e\ e>a\ and\ e>p\ ?$$ Statement 1 The sum of the balances on his everywhere cared and American card is $1350 and 3times the balances on his passport card....


Re: David has 3 credit cards: a Passport card, an EverywhereCard, and an American local card. He owes a balance on all t

let passport card = p ; everywhere card = e , and American card = a Target question= Does he get owe the greatest balance on everywhere card. $$i.e\ e>a\ and\ e>p\ ?$$ Statement 1 The sum of the balances on his everywhere cared and American card is $1350 and 3times the balances on his passport card....