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The charge for a telephone call between City R and City S is $0.42 for each of the first 3 minutes and $0.18 for each additional minute. A certain call between these two cities lasted for x minutes, where x is an integer. How many minutes long was the call? (1) The charge for the first 3 minutes of ...


This is a solid approach. If we're concerned about keeping track of units, dimensional analysis can help: $$1\ new\sec\left(\frac{1\ new\ \min}{100\ new\ \sec}\right)\left(\frac{1\ new\ hour}{100\ new\ \min}\right)\left(\frac{1\ day}{10\ new\ hours}\right)\left(\frac{24\ hours}{1\ day}\right)\left(\...


The key thing to notice here is that the problem does not say that the number of shares increased BY 10,000,000 — it says that the number of shares increased TO 10,000,000. So at the end of the year, there are only 10,000,000 shares. So for the first 9 months, the corporation earned money on all 5...

by ErikaPrepScholar

Sat Mar 31, 2018 3:14 pm
Forum: Problem Solving
Topic: A corporation with 5,000,000 shares of publicly...
Replies: 3
Views: 657

Three-digit passwords can begin with 0. So options like 011, 076, 002, and 000 are all valid passwords. This gives 10 options for each digit, or 10*10*10=10^3 possibilities in total.

by ErikaPrepScholar

Sat Mar 31, 2018 3:05 pm
Forum: Problem Solving
Topic: How many three-digit passwords are possible on a home
Replies: 2
Views: 463

First, we want to address issues of parallelism and sentence structure. In A, B, and C, we have "By recording ... and then digitizing and analyzing ..., a team of scientists ..." "recording", "digitizing", and "analyzing" are all things that the team did, and they are all parallel. However, in D and...


Another issue with B that hasn't been addressed: we do not know that the construction of an oil pipeline across the lake's bottom will affect land use and drainage patterns around the lake. 1) Pipeline is at the bottom of the lake, not around the lake. 2) There is no clear connection between the pip...

by ErikaPrepScholar

Sat Mar 31, 2018 2:42 pm
Forum: Critical Reasoning
Topic: Lake Konfa
Replies: 7
Views: 4293

First, the noun "firm" is singular, as indicated by the pronoun "its" earlier in the sentence. So we can rule out A and C for using "their". By integrating its two pharmaceuticals divisions, the firm will increase their share of the nation’s $135 billion healthcare market from 5 percent to 9 perce...


We can start by eliminating A and B. First, the proper noun form of reduce is "reduction" not "reducing". Second, this sentence says that "reducing ... fails to recognize...". The act of reducing something cannot recognize or fail to recognize something. The Finance Board can recognize or fail to re...


We can approach this a couple ways. If we know that "like" must compare nouns, while "as" must compare verbs, we can eliminate C, D, and E immediately. To decide between A and B, we can think about the meaning. Is Ariba "just like" many neighboring regions? Or is it only "like" its neighboring regio...


This sentence COMPARES two things. When we compare things, we want them to be parallel. The first thing in our comparison is $40 billion dollars in 2013 So our structure is dollar amount at some time Looking through our answers, we can eliminate A, D, and E for spoiling the parallelism (note: "in la...


I can answer this one for you: this is a PrepScholar question, and the OA is B . First off, we can eliminate C, D, and E. "and therefore may have studied the works of other cultures" must refer to "the early Greeks". However, in the last three answers, the subject of the sentence is "temples". Decid...


Raising any positive or negative number to an even power will yield a positive number. Raising a negative number to an odd power will yield a negative number. Statement 1 $$m^5n^2<0$$ n^2 must be positive whether n is positive or negative. This means that for the whole expression to be negative, m^5...

by ErikaPrepScholar

Sat Mar 31, 2018 1:14 pm
Forum: Data Sufficiency
Topic: Is mn < 0?
Replies: 3
Views: 517

We want to know if abcd is negative. We know that a negative times a negative is a positive, so for abcd to be negative, 1 or 3 of the variables must be negative. If 0, 3, or 4 variables are negative, then abcd will be positive. (Note: if any of the variables are 0, then abcd will be 0.) Statement 1...

by ErikaPrepScholar

Sat Mar 31, 2018 1:06 pm
Forum: Data Sufficiency
Topic: Is the product abcd negative?
Replies: 3
Views: 373

Comment for swerve: We do not know that a < b < c. We only know that a is the shortest building, meaning that b and c must be taller than a. However, we do not know that c is taller than b — they could be the same height and both be taller than a. Thus, buildings b and c could have the same height...


$$x^2+6x+9=\left|x+3\right|$$ The absolute value gives us two options: $$x^2+6x+9=x+3$$ or $$x^2+6x+9=-\left(x+3\right)$$ $$x^2+6x+9=-x-3$$ Solving each individually: $$x^2+6x+9=x+3$$ $$x^2+5x+6=0$$ $$\left(x+2\right)\left(x+3\right)=0$$ $$x=-2\ and\ x=-3$$ and $$x^2+6x+9=-x-3$$ $$x^2+7x+12=0$$ $$\l...

by ErikaPrepScholar

Sat Mar 31, 2018 11:48 am
Forum: Problem Solving
Topic: What is the sum of all unique solutions for
Replies: 2
Views: 346