Эффективные уроки GMAT. Inequalities with absolute value
В некоторых заданиях теста мы столкнемся с необходимостью решить неравенство с модулем. Такие задания обычно относят к сложным, хотя использование нескольких простых формул сводит их к алгоритмическим действиям.
Some problems on GMAT contain inequalities with absolute value. These tasks may seem hard but some easy formulae can help you to get the right answer very fast.
To solve an inequality with the absolute value you need to remember two simple rules:
1. Is |x - 1| < 1?
(1) (x - 1)2 d 1
(2) x2 - 1 > 0
(A) Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient
(B) Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient
In fact, we are asked if -1< x-1< 1 or if 0< x< 2.
Statement
(1) is equivalent to |x - 1| d 1 or 0d xd 2 . If x = 0 or x = 2,
statement (1) holds but the principal statement is not true. Statement
(2) is not sufficient either. If x = 1.5 the principal statement holds
but if x is big, say 5, the principal statement is not true. Although
Statement (2) means that x cannot be 0 it does not exclude the
possibility of x being 2. Thus, Statement (1) and Statement (2)
combined are not sufficient to answer the question. The answer is E.
2. Is |x - 5| > 4 ?
(1) x is an integer
(2) x2 < 1
(A) Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
(B) Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient
This question becomes incredibly easy if we rewrite it:
|x-5|>4 is the same as x-5>4 or x-5<-4, so the question is if x9.
Statement
(1) doesn't help at all. Statement (2) is sufficient for it means that
x is confined between -1 and 1 and thus its true that x<1. The
answer is B.
3. How many integers X are there so that |X - 3.5| < 2?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
This
inequality can be rewritten as -2
This lesson shows some typical problems, in which
inequalities with the absolute value appear, and the most effective
ways to solve them in 2 minutes or even faster and add some points to
your GMAT total score.
Material prepared by Ksenia Zueva, GMAT consultant at MBA Strategy
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