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If x and y lie on the number line shown above, which of the following

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If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 12 Jul 2017, 01:31
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A
B
C
D
E

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If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 12 Jul 2017, 01:51
Bunuel wrote:
Image
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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Re: If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 13 Jul 2017, 06:31
Bunuel wrote:
Image
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
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Re: If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 13 Jul 2017, 07:06
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Bunuel wrote:
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

Based on the figure given and fractions,

A) 1/y > 2 - 1/Y is always less than 2 because y>1/2 - Incorrect
B) 1/X <2 - 1/X is always greater than 2 because X<1/2 - Incorrect
C) 1/X < 1/Y - incorrect because it implies Y<X
D) X+y <1 May or May not be <1(e.g. 09+04 etc).
E) XY<1/2 - Always because 1/2*1 is 1/2. A smaller fraction (x) of smaller number (y) will always be less than 1/2.
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If x and y lie on the number line shown above, which of the following  [#permalink]

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New post Updated on: 15 Jul 2017, 07:56
I've just made the inequalities look more comfortable and picked up numbers for x and y (x=1/4 ; y=3/4)

(A) 1/y >2 --- 1>2y -- 1>2*3/4 -- 1>3/2? -- Clearly false.
(B) 1/x <2 --- 1<2x -- 1<2*1/4 -- 1<1/2? -- False.
(C) 1/x < 1/y --- y<x -- 3/4<1/4? -- Clearly false.
(D) x+y < 1 --- y<1-x --- 3/4<1-1/2 -- 3/4<1/2? -- False
(E) xy < 1/2 -- y<1/2x --- 3/4<1/(2*1/2) --- 3/4 < 1? -- True

Hence (E)

Originally posted by sergioas22 on 14 Jul 2017, 16:56.
Last edited by sergioas22 on 15 Jul 2017, 07:56, edited 2 times in total.
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Re: If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 15 Jul 2017, 07:11
Using x=1/4 and y=3/4
only xy < 1/2 this inequality is satisfied. So answer is E
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Re: If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 15 Jul 2017, 08:08
If x coincided with 1/2 and y coincided with 1, xy would have been 1/2. But, we know that both variables are on the left hand side of the assumption.

Hence E is the right choice!
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Re: If x and y lie on the number line shown above, which of the following  [#permalink]

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New post 16 Jul 2017, 17:27
Bunuel wrote:
Image
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


We see that 0 < x < 1/2 and 1/2 < y < 1. Thus, 1/x > 2 and 1 < 1/y < 2. Therefore, answer choices A, B, and C are wrong.

Answer choice D is not correct either, since if x = 2/5 and y = 4/5, then x + y = 6/5 > 1. Thus, answer choice E must be correct. In fact, since x is a positive number less than 1/2 and y is a positive number less than 1, the product of x and y must be less than 1/2 * 1 = 1/2.

Answer: E
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Re: If x and y lie on the number line shown above, which of the following   [#permalink] 16 Jul 2017, 17:27
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If x and y lie on the number line shown above, which of the following

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