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# If the line ax + by = 1 has its y-intercept greater than its x-interce

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Manager
Joined: 08 Apr 2017
Posts: 77
If the line ax + by = 1 has its y-intercept greater than its x-interce  [#permalink]

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28 May 2018, 18:08
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2
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Difficulty:

95% (hard)

Question Stats:

32% (02:21) correct 68% (02:30) wrong based on 49 sessions

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If the line ax + by = 1 has its y-intercept greater than its x-intercept, then which of the following must be true? (Given ab not equal to 0)

i. ab > 1

ii. a > b

iii. a > -b

A. i only

B. ii only

C. i & ii only

D. ii & iii only

E. none
Math Expert
Joined: 02 Aug 2009
Posts: 7754
Re: If the line ax + by = 1 has its y-intercept greater than its x-interce  [#permalink]

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28 May 2018, 19:06
GMATSkilled wrote:
If the line ax + by = 1 has its y-intercept greater than its x-intercept, then which of the following must be true? (Given ab not equal to 0)

i. ab > 1

ii. a > b

iii. a > -b

A. i only

B. ii only

C. i & ii only

D. ii & iii only

E. none

So we just know y>X..
So many variables where a and b depend on y and x, we can almost be sure that all values are possible for a and b, so nothing is MUST..

But let's check
ax+by=1..
I) ab>1
Say x = 2 and y=4, both a and b can be <1 so ab<1 in these cases..
Need not be MUST
II) a>b
Say x = -3 and y=-2, X can be -5 and y can be 7
(-3*-5)+(-2*7)=15-14=1....a<b
Not true always
III) a>-b
Same case above
X=-3 , y=-2.... x can be 5 and y can be -8
(-3*5)+(-2*-8)=-15+16=1
But 5<-(-8)
So again need not be MUST

E
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Manager
Joined: 21 Jun 2017
Posts: 226
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: If the line ax + by = 1 has its y-intercept greater than its x-interce  [#permalink]

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24 Dec 2018, 21:28
1
X-intercept =1/a Y-intercept =1/b
Stem ----> 1/b - 1/a > 0
Or (a-b)/ab > 0
So i) a>b and ab>0 or ii) a<b and ab<0
Since this is a must be true question, none of the options is always true.
E

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Re: If the line ax + by = 1 has its y-intercept greater than its x-interce   [#permalink] 24 Dec 2018, 21:28
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