Search found 1780 matches


Re: In a certain factory, the union membership was higher in 2010 than in 2008. For the period from 2007 to 2011, the

When finding the correct answer choice that strengthens the argument in this question, it should be noted that the answer must be directly relevant to the specific argument in question. Also, it must provide information that justifies the argument. Premise: The union membership was higher in 2010 th...


Re: Herbal tea has become a popular product and is offered by a number of brands. An investigation showed that out of th

In finding the answer choice that strengthens the argument in this question, it should be noted that the answer must be directly relevant to the specific argument in question. Furthermore, it must also provide information that justifies the argument (in this case, To drink a truly healthy herbal tea...


Re: How many integrals value of \(x\) satisfy the inequality \((1-x^2)(4-x^2)(9-x^2) > 0 ?\)

$$\left(1-x^2\right)\left(4-x^2\right)\left(9-x^2\right)>0$$ $$\left(1-x^2\right)=\left(1+x\right)\left(1-x\right)$$ $$\left(4-x^2\right)=\left(2+x\right)\left(2-x\right)$$ $$\left(9-x^2\right)=\left(3+x\right)\left(3-x\right)$$ $$Therefore,\ \left(1+x^2\right)\ \left(4-x^2\right)\ \left(9-x^2\right...


Re: If \(5^x-5^{x-3}=124\cdot 5^y,\) what is y in terms of \(x?\)

$$5^x-5^{x-3}=124\cdot5^y$$
$$factorizing\ 5^x-5^{x-3}$$
$$5^{x-3}\cdot\left(5^3-1\right)=124\cdot5^y$$
$$5^{x-3}\cdot\left(25-1\right)=124\cdot5^y$$
$$x-3=y$$
$$y=x-3$$
$$Answer\ =\ C$$


Re: In a survey on three products – A, B, and C – 50% of those surveyed liked product A, 30% liked product B, 20% liked

% of those that like A = 50% % of those that like B = 30% % of those that like C = 20% % of those that liked all 3 products = 5% % of those that liked at least one of the 3 products = 85% Total % = % of A + % of B + % of C - % of those who like 2 products - 2 (% of those who like 3 products) + % of ...


Re: Roxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the dur

Given that: p = 2000 Total interest in 6 years = 4000 Money in the account after 6 years = 2000 + 4000 = 6000 Hence, money in the account is going to be; principal * 3 every 6 years Target question => After how many years of investment did she earn a total interest of $52000? Let the number of years...


Re: If \(\$1\) was invested at \(4\%\) interest, compounded quarterly, the total value of the investment, in dollars, at

Given that: principal = $1, interest = 4% Time = 3 years, n = 4 (compounded quarter) $$A=P\cdot\left(1+\frac{r}{n}\right)^{\left(t\cdot n\right)}$$ $$A=1\cdot\left(1+\frac{4}{4}\div100\right)^{\left(3\cdot4\right)}$$ $$A=\left(1+1\cdot\frac{1}{100}\right)^{\left(12\right)}$$ $$A=\left(1+0.01\right)^...


Re: The sides of a square region, measured to the nearest centimeter, are 6 centimeters long. The least possible value o

A square has 4 equal sides, given that the sides are measured to the nearest centimeters as 6cm $$Let\ 1\ side=x$$ $$5.5cm\ \le x\le6.4cm$$ This means the length of a side of the square can be any value between 5.5cm and 6.4cm because any value in this range can be rounded to 6.0cm as the nearest Th...


Re: A customer purchased 6 shirts priced at $10.99 each, excluding sales tax. How many sales tax did he pay on this purc

Given that: Price of 1 shirt without sales tax = $10.99 -Price of 6 shirts without sales tax = 6 * 10.99 = $60.99 Target question => How much tax did he pay on this purchase? Statement 1 => The customer paid a 5% sales tax on the total price of the shirts Therefore, sales tax = 5% of $60.99 =5/100 ...


Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate give

For Kate to have more than $10 and Danny to have less than $15 the fair coin must land on head 3 or 4 times However, the fair coin has 2 sides and it is flipped 5 times $$Total\ number\ of\ possibilities\ =\ 2^5=32$$ $$probability\ of\ getting\ 3\ heads\ =\ \frac{5C3}{32}$$ $$where\ 5C3=\frac{5!}{3!...


Re: The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

Given that: x + y = 65 feet Target question => How long is the shorter price? Statement 1 => The length of the pieces of rope are 8:5 $$x+y=65............eqn1$$ $$x:y=8:5$$ $$\frac{x}{y}=\frac{8}{5}$$ $$5x=8y\ and\ x=\frac{8y}{5}$$ $$Substitute\ x\ in\ eqn\ 1$$ $$x+y=65\ \ \ \ \ where\ x=\frac{8y}{...


Re: The price of each hair clip is ¢ 40 and the price of each hairband is ¢ 60. Rashi selects a total of 10 clips and ba

Given that: - price of each clip = ¢ 40 - price of each hairband = ¢ 60 - the average price of (10 clip and band) = ¢ 56 Let the number of clips purchased = c Number of hairband = 10 - c Price of total clips = 40 * c = 40c Price of total hairbands = 60 * (10 - c)= 600 - 60c $$Average\ price\ =\frac{...


Re: \(S\) is a sequence \(s_1, s_2, s_3, \ldots, s_n\) in which every term after the first is one less than three times

$$Let\ s_1=x$$ $$s_2=3x-1$$ $$s_3=3\left(3x-1\right)-1=9x-3-1=9x-4$$ $$s_4=3\left(9x-4\right)-1=27x-12-1=27x-13$$ $$s_5=3\left(27x-13\right)-1=81x-39-1=81x-40$$ $$Given\ that\ \ s_5-s_3=28$$ $$\left(81x-40\right)-\left(9x-4\right)=28$$ $$81x-40-9x+4=28$$ $$81x-9x=28+36$$ $$\frac{72x}{72}=\frac{64}{7...


Re: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the gr

Total student => 232 Students that took geometry => 144 Students that took biology => 119 Greatest possible number of students taking both geometry and biology = possibility that all the students that took biology also took geometry Greatest possible number of students taking both => 119 For the sma...


Re: Members of a social club met to address 280 newsletters. If they addressed 1/4 of the newsletters during the first h

Total newsletter = 280 During the first hour, they addressed 1/4 of total newsletters => 1/4 * 250 = 70 newsletters After the first hour, newsletters remain => 280 - 70 = 210 During the second hour, they addressed 2/5 of the remaining newsletters => 2/5 * 210 = 2 * 42 =>84 newsletters Answer = D