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1) In an exam, 40% of the students failed English, 30% failed Math, and 20% failed Science.. 10% of the students failed both English and Math; 5% failed in both Math and Science. No one failed both English and Science . What percent of the students passed all three subjects ?
(A) 30% (B) 25% (C) 20% (D) 15% (E) 10%
 Hints.
Find the percentage of the students who failed at least one subject and then look at the options very closely. Can you see the correct answer? Of course you can .
2) Is x = y ? x and y are non-zero integers .
(A) Statement-1 by itself is sufficient to answer the question ,but statement-2 by itself is not ;
(B) Statement-2 by itself is sufficient to answer the question, but statement-1 by itself is not ;
(C) Statement-1 and statement-2 taken together are sufficient to answer the question, even though neither statement by itself is sufficient .
(D) Each of the statements by itself is sufficient to answer the question.
(E) Statements 1) and 2), even taken together , are not sufficient to answer the question, requiring more data pertaining to the problem.
Hints.
Statement-1 alone is not sufficient because for both x = y and x = - y , given the statement is true .This means , “YES( x = y)” is an answer and “NO( x?y)” is an answer too . Such an ambiguous case can not be a correct answer . Is it possible to draw a similar conclusion for statement-2 ? May be . So , the correct answer should be (B), (C) or (E) . Would you like to guess ? Your chance is 33~ % .
ANSWERS: Problem 1 Answer is B
Problem 2 Answer is E
Is this what you came up with?
Professor Ali is the Math teacher for Pericles. To learn more about our GMAT; TOEFL; or MBA Advising please contact us at 292-5188/6463, or write to us at info@pericles.ru or just look at our website at www.pericles.ru.
Автор: Professor Ali is the Math teacher for Pericles.
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