If a/b c/d 1, which of the following could be true about the recip

Question

If  \frac{a}{b}>\frac{c}{d}>1 , which of the following could be true about the reciprocals of a, b, and c ?

A.  \frac{1}{a}>\frac{1}{b}>0>\frac{1}{c}>\frac{1}{d}

B.  \frac{1}{b}>\frac{1}{a}>0>\frac{1}{c}>\frac{1}{d}

C.  \frac{1}{b}>\frac{1}{a}>0>\frac{1}{d}>\frac{1}{c}

D.  \frac{1}{c}>\frac{1}{a}>0>\frac{1}{b}>\frac{1}{d}

E.  \frac{1}{d}>\frac{1}{c}>0>\frac{1}{b}>\frac{1}{a}

yashikaaggarwal · Answer

let say a = 3 and b =2
reverse of positive integer
if +b<+A (2<3)then 1/b > 1/a (1/2 > 1/3)

or if -B>-A (-2>-3) then 1/-b < -1/a (-1/2<-1/3)

a/b>c/d>1
we can say a>b and c>d (positive values)
So if a and b are positive.
1/b > 1/a or if negative 1/b < 1/a

none of the option have a and b as negative option. (eliminate D and E)
among A,B and C
only B and C satisfy 1/b > 1/a
A eliminate.

if c and d are are negative 1/c>1/d
B is satisfying all.

IMO B

jhaamod10 · Answer

a/b>1 If a>0 then b>0 & a>b Hence 1/a<1/b Now c/d>1 If c<0 then d<0 & c1/c>1/d If a=5 b=2 c=-4 & d=-3 Then 1/b>1/a>0>1/c>1/d Hence possible option is B Posted from my mobile device

jamil007 · Answer

when it is above 0, 1 divided by bigger number is smaller.
when it is below 0, 1 divided by bigger number is bigger (by bigger I mean -5 is bigger than-4)

so answer is C

lordvoldemort123 · Answer

IF YOU ARE WEAK IN QUANTS, YOU CAN REFER TO THIS EXPLANATION

To begin with,
Take easy fractions.

1+1/2= 3/2
1+ 1/4= 5/4

We have the condition given to us as:
3/2 > 5/4 > 1

here
a=3
b=2
c=5
d=4

but the twist and an important thing here is,
in all the options mentioned below 0 is shown greater than two fractions.

which of the 4 values mentioned can be negative ?
we have to keep in mind that choosing a variable as negative should also satisfy the condition mentioned above
i.e

a/b > c/d > 1

what if i choose a and c as negative
then the above equality wont satisfy.

Hence,
we have to either choose a and b both as negative so that we get fraction a/b as positive
or
we have to choose c and d both as negative, so that again we get fraction c/d as positive.

So now lets assume

in my equation, c and d as negative.

3/2 > (-5)/(-4) > 1

here
a= 3
b= 2
c= -5
d= -4

since a>b

therefore 1/b>1/a, that is; 1/2>1/3

this will follow for c and d as well

therefore one may assume it to be 1/d>1/c ; [1/(-4) > 1/(-5)] also can be written as [-0.25 and -0.20]
but these are negative fractions.
so please keep in mind that value of -0.25 is less than -0.20

Hence here we will have 1/c>1/d

Hence Our final comparison is

1/b>1/a>0>1/c>1/d

i.e answer option B.

Lets wait for the OA

Adarsh_24 · Answer

Here's my thinking

When we look at this question.

We can see,
a/b > 1

we need to know that this can happen in couple of ways.
eg:-8/-4 or 8/4
Same sign and numerator always has bigger absolute value.

Now looking at options we can notice 2 things,
1. its in an order. here descending
2. couple of reciprocals are negative.

In a reciprocal only 1 variable is involved. So that variable should have same sign as reciprocal. So 2 variables are -ve.
So 2 combinations i can think of

1) 12/4 > -2/-1 > 1

a=12 -> 1/a = 1/12
b=4 -> 1/b = 1/4
c=-2 -> 1/c = -1/2
d=-1 -> 1/d = -1

arranging in descending order
1/b>1/a>0>1/c>1/d
Option B matches it.

2) -12/-4 > 2/1 > 1
No need to check this. But, anway let's assume we had taken this first instead and proceed.
a=-12 -> 1/a = -1/12
b=-4 -> 1/b = -1/4
c=2 -> 1/c = 1/2
d=1 -> 1/d = 1

So desending order will be
1/d>1/c>0>1/a>1/b
No such combination available.

TtTt1212 · Answer

Hi  Bunuel  why is D incorrect?

Bunuel · Answer

D implies that a and c are positive, while b and d are negative. This would make a/b and c/d negative, thus violating the given condition that they are positive ( \frac{a}{b} > \frac{c}{d} > 1 ).

TtTt1212 · Answer

Oh I get it now, thanks so much!

Akshaynandurkar · Answer

a/b > 1
then a>b if both are positive. In this case 1/a < 1/b > 0
or a<b if both are negative. In this case 1/a > 1/b < 0

c/d >1
then c>d if both are positive. In this case 1/c < 1/d > 0
or c<d if both are negative. In this case 1/c > 1/d < 0

combining 1st inference with 4th inference we can conclude that
1/b > 1/a > 0 > 1/c > 1/d

If a/b > c/d > 1, which of the following could be true about the recip

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