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Viewer: Photo | Video | Audio Browser, Loupe View, Full Screen, Flag, Star Rating, Lossless Rotate, Share (Email,Twitter,Facebook), Metadata (Exif,IPTC, GPS) Viewer.Here, it means a is no more than b, but if b is strictly less than c, so does a. That is because in a < b ≤ c, it says b is no more than c, so if a is strictly less than b, it will be also strictly less than c, hence the conclusion inequality a < c. The reason is we always take the sign of the < (“strictly less than”) sign when a double inequality have both. So your question is, if a double inequality have both < and ≤ signs, why we take the < sign, instead of the ≤ sign? You can see that the premise actually can be combined into a double inequality, that is, for short, we can say: a < b < c implies that a < c a ≤ b ≤ c implies that a ≤ c and last but not least, a < b ≤ c implies a < c. Of course, here we have if a < b and b ≤ c, then a < c. Another example is: if a ≤ b and b ≤ c, then a ≤ c. It’s a transitive property in inequalities.įor example, if a < b and b < c, then a < c. Thus, answer D conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.įirst of all, we are NOT adding the two inequalities to arrive to the conclusion that x < 5. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. Since we have 1 variables and 0 equations, D is most likely to be the answer and so we should consider each of conditions first. Remember that equal numbers of variables and independent equations ensure a solution. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. The answer to the target question is YES, x is less than 5, which means statement 2 is SUFFICIENTįorget conventional ways of solving math questions. We can add this information to our existing inequality to get: x < 5 - x² ≤ 5Īt this point, we can clearly see that x < 5 So, when x is 0, the expression 5 - x² = 5įor all other values of x, we know that 5 - x² < 5 Since x² is always greater than or equal to 0, the GREATEST possible value of 5 - x² is 5, and this occurs when x = 0 Subtract x² from both sides of the inequality to get: x < 5 - x² Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT Here are two:Ĭase a: x = -10, in which case the answer to the target question is YES, x is less than 5Ĭase b: x = 10, in which case the answer to the target question is NO, x is not less than 5 There are several values of x that satisfy statement 1.