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12 Jul 2017, 01:31
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If x and y lie on the number line shown above, which of the following statements must be true?
(A) 1/y > 2
(B) 1/x < 2
(C) 1/x < 1/y
(D) x + y < 1
(E) xy < 1/2
Attachment:
2017-07-12_1229.png [ 3.33 KiB | Viewed 6579 times ]
12 Jul 2017, 01:51
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Bunuel
If x and y lie on the number line shown above, which of the following statements must be true?
(A) 1/y > 2
(B) 1/x < 2
(C) 1/x < 1/y
(D) x + y < 1
(E) xy < 1/2
Attachment:
2017-07-12_1229.png
It should be E.
A- 1/y would be greater than 2 if y was less than 0.5 but this is not the case since 1/2 < y < 1.
B- Conversely 1/x would be less than 2 if x was greater than 0.5 which is not the case.
C- 1/x would be less than 1/y if x > y but we know x is actually less than y. flipping fraction for x and y would flip the inequality between them.
D- We cannot be certain about this. If x = 3/10 and y = 9/10, x+y would be greater than 1 while both still satisfy the conditions.
E- Say we assume y as close to 1 as possible. 99/100 or 0.99, x cannot be greater than 0.5 or 1/2. so xy has to be less than half of y since multiple x is less than half. 1/2 of y is of course less than 1/2 since y < 1.
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13 Jul 2017, 06:31
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Bunuel
If x and y lie on the number line shown above, which of the following statements must be true?
(A) 1/y > 2
(B) 1/x < 2
(C) 1/x < 1/y
(D) x + y < 1
(E) xy < 1/2
Attachment:
2017-07-12_1229.png
I will try to DISPROVE each statement by plugging numbers
Let x = 1/4 & y =3/4
(A) 1/y = 4/3 Not greater than 2B) 1/x < 2 ...........Eliminate
B) 1/x = 4 Not less than 2 B) 1/x < 2 ...........Eliminate
(C) 1/x < 1/y...... 4 < 4/3 ...........Eliminate
(D) x + y < 1...1/4 + 3/4 = 1....... ...........Eliminate
(E) xy < 1/2................No need to test
Answer: E
