![\"GMAT](\"https:\/\/magoosh.com\/gmat\/files\/2012\/03\/image-gmat-header-ratios.jpg\")
<\/p>\n<\/p>\n
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\n
(A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.<\/ul>\n<\/ul>\n
\n
(B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.<\/ul>\n<\/ul>\n
\n
(C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.<\/ul>\n<\/ul>\n
\n
(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
![\"p_1\/r_1](\"https:\/\/magoosh.com\/gmat\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_977_b50b32091bcd33a40599940370341b06.png\" "\\"p_1\/r_1")
<\/p>\n