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Among other things, this post is a case study of an OG DS question:<\/p>\n
OG 12th Edition, Data Sufficiency Practice Problem #23<\/em><\/p>\n Here is the problem that appears in the OG:<\/p>\n 23) If p1<\/sub> and p2<\/sub> are the populations and r1<\/sub> and r2<\/sub> the number of representatives of District 1 and District 2 respectively, the ratio of the population to the number of representatives is greater for which of the following districts?<\/p>\n (1) p1<\/sub>>p2<\/sub><\/p>\n (2) r2<\/sub>>r1<\/sub><\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n Below, I’ll show the solution to this.<\/p>\n <\/p>\n Here are two very important fraction rules.<\/p>\n 1) When the numerator increases and the denominator stays the same, the fraction as a whole increases.\u00a0 When the numerator decreases and the denominator stays the same, the fraction as a whole decreases.<\/p>\n 2) When the denominator increases and the numerator stays the same, the fraction as a whole decreases.\u00a0 When the denominator decreases and the numerator stays the same, the fraction as a whole increases.<\/p>\n <\/p>\n Those, as they are stated, are always true 100% of the time.<\/p>\n <\/p>\n If both the numerator and denominator change at the same time, then things are trickier.\u00a0 See the table below, which assumes that both numerator and denominator are positive.<\/p>\n Numerator<\/strong><\/p>\n<\/td>\n Denominator<\/strong><\/p>\n<\/td>\n Fraction as a Whole<\/strong><\/p>\n<\/td>\n<\/tr>\n increases<\/p>\n<\/td>\n increases<\/p>\n<\/td>\n \u00a0(all bets are off<\/em>)<\/p>\n<\/td>\n<\/tr>\n increases<\/p>\n<\/td>\n decreases<\/p>\n<\/td>\n \u00a0increases<\/p>\n<\/td>\n<\/tr>\n decreases<\/p>\n<\/td>\n increases<\/p>\n<\/td>\n decreases<\/p>\n<\/td>\n<\/tr>\n decreases<\/p>\n<\/td>\n decreases<\/p>\n<\/td>\n \u00a0(all bets are off<\/em>)<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n In the first case, for example, whether the fraction increases depends on how much<\/em> the numerator increases, and how much<\/em> the denominator increases.\u00a0 For example:<\/p>\n 1\/3 -> 2\/5\u00a0\u00a0 both numerator & denominator increase, and fraction increases<\/p>\n 1\/3 -> 2\/7\u00a0\u00a0 both numerator & denominator increase, and fraction decreases<\/p>\n (Both of those can be easily seen from the fact that 1\/3 = 2\/6, so be increasing or decreasing the denominator of 2\/6, we can create bigger or smaller fractions.)<\/p>\n <\/p>\n Now, we can tackle the DS problem above.\u00a0 We are comparing fractions of population over number of representative, p\/r.<\/p>\n\n
(A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.<\/ul>\n<\/ul>\n
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(B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.<\/ul>\n<\/ul>\n
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(C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.<\/ul>\n<\/ul>\n
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(D) Each statement alone is sufficient to answer the question.<\/ul>\n<\/ul>\n
(E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.<\/ul>\n
Basic Fraction Facts<\/h2>\n
Not As Simple<\/h2>\n
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\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n Back to the OG DS Problems<\/h2>\n
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