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

implex

Quote:

Originally Posted by Aarav

This wouldn't be that straight -> someone who can solve this on his/her alone has to be a genius. Please treat this as a recreational problem than anything else.
But, I will urge each one of you to have a crack at this -> if not alone then you can collectively come out with a solution to this. Use of calculators, excel sheets is all allowed

yeah, looks like some project !!
there are quite so many cases especially with the rounding off of .5

I am not able to sit down that calmly which this problem requires. But I know it's too cool a problem to be cracked in few gos!

siddooba

Quote:

Originally Posted by Aarav

Ok -> this is the warm-up problem since I want Implex also to have a go at this

This is last year's QQAD problem that took Vineet, me and a friend of mine in Intel research team to come to any conclusion in 4 hours. Treat this as a warm up and real contest (easy + difficult problems) with points will be held tomorrow.

Allwin likes to talk only in integer numbers. So much that he rounds off everything including his course average points to the nearest integer. For example, 89.34 is 89 and 99.54 is 100, and 115.5 is 116. Allwin always calculates the average (real) on the cumulative points so far. After his 75 points in Finance, his rounded average drops by 1 point. Next, after 83 points in strategy paper, his rounded average further plummets down by 2 points. Which among the following is not true?

(a) The minimum possible number of courses is less than 15
(b) The maximum possible number of courses is not more than 50
(c) The minimum possible current rounded average is 95
(d) Either of 126 or 127 can be the current rounded average
(e) none of the foregoing

False : (b) The maximum possible number of courses is not more than 50

Number of Subjects: 51
Average: 150
Average after Finance: 148.558 (149)
Average after Strategy: 147.321 (147)

I tried doing it mathematically but not gaining much ground ..

srikar2097

Quote:

Originally Posted by Aarav

Ok -> this is the warm-up problem since I want Implex also to have a go at this

This is last year's QQAD problem that took Vineet, me and a friend of mine in Intel research team to come to any conclusion in 4 hours. Treat this as a warm up and real contest (easy + difficult problems) with points will be held tomorrow.

Allwin likes to talk only in integer numbers. So much that he rounds off everything including his course average points to the nearest integer. For example, 89.34 is 89 and 99.54 is 100, and 115.5 is 116. Allwin always calculates the average (real) on the cumulative points so far. After his 75 points in Finance, his rounded average drops by 1 point. Next, after 83 points in strategy paper, his rounded average further plummets down by 2 points. Which among the following is not true?

(a) The minimum possible number of courses is less than 15
(b) The maximum possible number of courses is not more than 50
(c) The minimum possible current rounded average is 95
(d) Either of 126 or 127 can be the current rounded average
(e) none of the foregoing

Posting my approach. I feel it's far from being correct, but it'll get things moving...

x-subjects; y-cumulative score so far; A-average so far.

A=y/x ---->1
A-1=(y+75)/(x+1) --->2
A-3=(y+15eight)/(x+2) ---->3

From 2 we get x^2 + 76x-y=0
from 3 we get 3x^2 +164x-2y=0
On solving, x=12; y=1056. These are the base initial values. ---->4

so the value of A = 88
By this (A-1) in 2 has to be 87 and (A-3) has to be 85

But by using the above got values of (x,y) I get (A-1) = 94.25 = 94
and (A-3) = 101.16 = 101

Clearly there is an offset in each of these values. Which is caused by Allwin's obsession of rounding off...

Actually after this I'm stuck...

srikar2097

Quote:

Originally Posted by siddooba

False : (b) The maximum possible number of courses is not more than 50

Number of Subjects: 51
Average: 150
Average after Finance: 148.558 (149)
Average after Strategy: 147.321 (147)

I tried doing it mathematically but not gaining much ground ..

Siddooba, how did you get subjects as 51? Not clear...

siddooba

Quote:

Originally Posted by srikar2097

Siddooba, how did you get subjects as 51? Not clear...

No I just assumed different combinations of subjects and average to try to prove any one of the 4 as false ..

eric.segal1

------------------------------------------------------
Quantitative Question # 034
------------------------------------------------------

In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?

(1) 736 (2) 768 (3) 792 (4) 840 (5) 876

in all the word can be arranged in 7! ways
now this 7! includes every possible arrangements of the 3 vowels.... but we need only one of the arrangements which has the sequence namely E....I....U so we gotta divide it by 3! ie 6
so final answer 7!/3!=840
answer is (4)

implex

Quote:

Originally Posted by srikar2097

Posting my approach. I feel it's far from being correct, but it'll get things moving...

x-subjects; y-cumulative score so far; A-average so far.

A=y/x ---->1
A-1=(y+75)/(x+1) --->2
A-3=(y+15eight)/(x+2) ---->3

From 2 we get x^2 + 76x-y=0
from 3 we get 3x^2 +164x-2y=0
On solving, x=12; y=1056. These are the base initial values. ---->4

so the value of A = 88
By this (A-1) in 2 has to be 87 and (A-3) has to be 85

But by using the above got values of (x,y) I get (A-1) = 94.25 = 94
and (A-3) = 101.16 = 101

Clearly there is an offset in each of these values. Which is caused by Allwin's obsession of rounding off...

Actually after this I'm stuck...

well you can't make equations, the problem has to be done in inequalities, the rounding off of the numbers at every stage, makes it impossible to make equations

suppose there are 5 subjects
and average is 10
then score is
(9.5)5<=S<(10.5)5

siddooba

Quote:

Originally Posted by srikar2097

Posting my approach. I feel it's far from being correct, but it'll get things moving...

x-subjects; y-cumulative score so far; A-average so far.

A=y/x ---->1
A-1=(y+75)/(x+1) --->2
A-3=(y+15eight)/(x+2) ---->3

From 2 we get x^2 + 76x-y=0
from 3 we get 3x^2 +164x-2y=0
On solving, x=12; y=1056. These are the base initial values. ---->4

so the value of A = 88
By this (A-1) in 2 has to be 87 and (A-3) has to be 85

But by using the above got values of (x,y) I get (A-1) = 94.25 = 94
and (A-3) = 101.16 = 101

Clearly there is an offset in each of these values. Which is caused by Allwin's obsession of rounding off...

Actually after this I'm stuck...

And regarding the part where I've bolded , A does not necessarily have to reduce by 1 for the first and similarly by 2 for the second.

When finance is added , the rounded average falls by 1 , but the actual drop can vary from 0.01 to 1.99. eg:

Minimum case: (An actual drop of 0.01)
Average = 125.5 (126)
After Finance is added = 125.49 (125)

Maximum case: (An actual drop of 1.99)
Average = 126.49 (126)
After Finance is added = 124.5 (125)

srikar2097

Quote:

Originally Posted by srikar2097

Posting my approach. I feel it's far from being correct, but it'll get things moving...

x-subjects; y-cumulative score so far; A-average so far.

A=y/x ---->1
A-1=(y+75)/(x+1) --->2
A-3=(y+15eight)/(x+2) ---->3

From 2 we get x^2 + 76x-y=0
from 3 we get 3x^2 +164x-2y=0
On solving, x=12; y=1056. These are the base initial values. ---->4

so the value of A = 88
By this (A-1) in 2 has to be 87 and (A-3) has to be 85

But by using the above got values of (x,y) I get (A-1) = 94.25 = 94
and (A-3) = 101.16 = 101

Clearly there is an offset in each of these values. Which is caused by Allwin's obsession of rounding off...

Actually after this I'm stuck...

Aarav, Am I on the right lines? Or do I need to take an entirely different approach?

siddooba

IMO , your equations should be ...

A=y/x ---->1
A-m=(y+75)/(x+1) --->2
A-n=(y+158 )/(x+2) --->3

where m can vary from 0<m<2
and n can vary from 2<n<4