CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

[ankursharma88]

what is an ordered pair ?
i did not even get the question ?
plz tell.
thanX.

[srikar2097]

Originally Posted by ankursharma88

what is an ordered pair ?
i did not even get the question ?
plz tell.
thanX.

ordered pair means (x,y) is different from (y,x) unless x=y.

[eric.segal1]

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Quantitative Question # 035
------------------------------------------------------

The number of ordered (x, y) such that 1/√x + 1/√y = 1/√20 is

(1) 1 (2) 3 (3) 5 (4) 7 (5) none of these


the answer is NONE OF THESE
actual answer m getting is 6

check out the attachment

solution.zip

....thats how i solved it
plz point me if m wrong

[eric.segal1]

Originally Posted by eric.segal1

------------------------------------------------------
Quantitative Question # 035
------------------------------------------------------

The number of ordered (x, y) such that 1/√x + 1/√y = 1/√20 is

(1) 1 (2) 3 (3) 5 (4) 7 (5) none of these


the answer is NONE OF THESE
actual answer m getting is 6

check out the attachment

Attachment 9812

....thats how i solved it
plz point me if m wrong

guys nowhere is it written that the ordered pair has to be an integer !!
In case that had been written then the answer will change....as we'll hv to further simplify all the six values and find out which ones are integrs....plz chek the attachment in my previous post above....u'll know exactly what m talking about

[siddooba]

Originally Posted by eric.segal1

guys nowhere is it written that the ordered pair has to be an integer !!
In case that had been written then the answer will change....as we'll hv to further simplify all the six values and find out which ones are integrs....plz chek the attachment in my previous post above....u'll know exactly what m talking about

Aarav corrected it in this post:
http://www.pagalguy.com/forum/quanti...tml#post114591 (CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions)

Integer values only ..

[Aarav]

Here's the 1st set of contest problems. Solve these for fun The next 2 sets will come at 11 am and 3 pm.

Set 1:

Problem 1:

Let a, b, c, d be distinct reals such that a + 1/b = b + 1/c = c + 1/d = d + 1/a = t then t equals

(a) Less than -1 (b) -1 (c) 0 (d) 1 (e) greater than 1


Problem 2:

Using three 6s and any mathematical operator, construct 10.


Problem 3:

Suppose numbers 1 to 20 are placed in any order around a circle. Show that sum of some 3 consecutive numbers must be at least 32.


Problem 4:

In an island, knights always tell the truth while knaves always lie. An islander Pavan, in the presance of another islander Slam said: "At least one of us is a knave". Is Pavan a knight or a knave. What about Slam?

[siddooba]

Slam -> Knave
Pavan -> Knight
Pavan said: "At least one of us is a knave"
=> Truth
=> Pavan is Knight
=> Possible

Slam -> Knave
Pavan -> Knave
Pavan said: "At least one of us is a knave"
=> True
=> Pavan is Knight
=> Contradiction

Slam -> Knight
Pavan -> Knave
Pavan said: "At least one of us is a knave"
=> Truth
=> Pavan is a knight
=> Contradiction

Slam -> Knight
Pavan -> Knight
Pavan said: "At least one of us is a knave"
=> False
-> Pavan is a knave
=> Contradiction

So Slam is a Knave and Pavan is a Knight

[siddooba]

a + 1/b = b + 1/c = c + 1/d = d + 1/a = t

a+b=bt

b+c=ct

c+d=dt

d+a=at
c/(t-1) + a = at
b/(t-1)^2 + a = at
a/(t-1)^3 + a = at
a/(t-1)^3 = a(t-1)

(t-1)^4 = 1

(c) t=0 is the solution

Edit : This solution is wrong - I've corrected my error in a later post.
t is greater than 1 (Root(2) to be exact)

[slam]

For Q-4

Pavan is either a knave or a knight.
case 1:
pavan is a knave => he lies => 'at least one of us is a knave' is false => none of them is a knave.
but pavan is a knave. => contradiction.

case 2:
pavan is a knight => he tells the truth => 'at least one of us is a knave' is true => slam is the knave (since pavan is not)

Going by this logic, case 2 would be correct.

[siddooba]

Ceiling {6 * log (6*6)}
= Ceiling { 9.338}
= 10

Edit:
(Root(6*6))\(.6) is a solution without floors or ceilings