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CAT 2007: Quantitative Questions a Day 51 to 100 - The Discussions

Please carry the QQAD discussion for the next 50 problems here. Try getting each and every solution in the very 1st attempt itself. Avoid risky speed. Just in case you see any mod around, please request him to make this thread sticky. ...
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Actually I M Not Getting Any Region Bounded By These Two Curves

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plz try to provide a diagram in he solutions to the geaometry and mensuration topics otherwise its real difficult to understand the sol

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ques# 105
solution for part A:
How many integral values of p are there for which the inequality 3 - x-p > x^2 is satisfied by at least one negative x?

"by atleast one negative x"
This implies whatever values of p we find for the solution x

taking x as negative the inequality looks like

3-(x+P)>x^2
or x^2+x+p-3

solving this we will get 2 roots. Now we have to see how x^2+x+p-3 will behave between these roots and beyong these roots. At x=-1/2 we will get minimum value of x^2+x+p-3. Thus any value between the roots satisfy the inequality. now on sloving the equation x^2+x+p-3 the delta value is 13-4p. For real values of the solution 13-4p>=0.
=> p
thus p can be any integral less than equal to 3. So the number of solutions will be infinite.
hence (e) non of the foregoing is the answer

check fallas. might be i m wrong

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Ques#105
Part B:

In the end of the question it says for all x in (1,2). This means x=1 for case 1and x=2 for case 2


case 1:
putting x=1 in the inequality we get
p^2+7*p+1
solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+7*p+1 will be less than zero (p= -7/2 will give ninimum value of the equation). Hence -6,-5,-4,-3,-2,-1 satisfy the inequality for x=1

case 2:
putting x=2 in the inequality we get
p^2+8*p+4
solving this using quadratic equation we will get 2 irrational values. The integral values between those 2 roots are -7,-6,-5,-4,-3,-2,-1. Between those 2 roots the value of p^2+8*p+4 will be less than zero (p= -4 will give ninimum value of the equation).
Hence -7,-6,-5,-4,-3,-2,-1 satisfy the inequality for x=1

The common integral values from case 1 and 2 are
-1,-2,-3,-4,-5,-6

thus, (d) 6 is the answer

Hope the solution is correct...have given major fundae:)

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sorry for an off topic but i had an inquiry about the CAT form that i have filled
I have made a mistake in the form

Name in the leaving certificate ----- Purohit Jitendra Bhomraj

the name i have written in the form in box 12 is
BOX 12 ----- Jitendra Bhomraj Purohit

i have not yet filled the BOX 1 in which the name is required
and also the name in BOX 1 should be the same as in the
school leaving certificate

the name in BOX 1 and BOX 12 must be in the same format

now what should i do

please help me

should i write the same name in BOX 1 that i have written in the BOX 12
to make the format same in both the boxes ignoring the name in the school leaving certificate
would that be alright


if u all cannot help me with that then please give some advice of where would i get the answer of my query


please help me as quickly as possible as i have to sent it to the IIM
as early as possible

:

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sorry for an off topic but i had an inquiry about the CAT form that i have filled
I have made a mistake in the form

Name in the leaving certificate ----- Purohit Jitendra Bhomraj

the name i have written in the form in box 12 is
BOX 12 ----- Jitendra Bhomraj Purohit

i have not yet filled the BOX 1 in which the name is required
and also the name in BOX 1 should be the same as in the
school leaving certificate

the name in BOX 1 and BOX 12 must be in the same format

now what should i do

please help me

should i write the same name in BOX 1 that i have written in the BOX 12
to make the format same in both the boxes ignoring the name in the school leaving certificate
would that be alright


if u all cannot help me with that then please give some advice of where would i get the answer of my query


please help me as quickly as possible as i have to sent it to the IIM
as early as possible

:

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Sorry, was in half sleep early morning and hence posted #104 on the wrong thread

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Quantitative Question # 104 (the answer for both Part A and Part B are in the same set of options)
------------------------------------------------------
Question(s):
(Part A)
A regular hexagon ABCDEF is inscribed in a circle with radius r. Another regular hexagon is formed (lying fully inside the circle with radius r) with 2 of its vertices internally on AB and another 2 on the circle. What is the ratio of the sides of the smaller hexagon to the larger hexagon?
(Part B)

In circle O, chords AB and AC are drawn so that AB = AC. Chord PQ is drawn intersecting AB and AC at points D and E respectively. D lies internally between E and P. Given AD = EC = 1/3 and DB = AE = 1/4, what is the maximum value of PD - QE?
(a) 1/18 (b) 1/12 (c) 1/13 (d) 1/6 (e) none of the foregoing


And 104 #

1. The answer is (c)
Not posting the figure but final expression using pythagoras,
13x^2 + 12xr - r^2 =0
x =r/13
The side of bigger hexagon = r
Hence (c)
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------------------------------------------------------
Quantitative Question # 104 (the answer for both Part A and Part B are in the same set of options)
------------------------------------------------------

Question(s):

(Part A)

A regular hexagon ABCDEF is inscribed in a circle with radius r. Another regular hexagon is formed (lying fully inside the circle with radius r) with 2 of its vertices internally on AB and another 2 on the circle. What is the ratio of the sides of the smaller hexagon to the larger hexagon?

(Part B)
In circle O, chords AB and AC are drawn so that AB = AC. Chord PQ is drawn intersecting AB and AC at points D and E respectively. D lies internally between E and P. Given AD = EC = 1/3 and DB = AE = 1/4, what is the maximum value of PD - QE?

(a) 1/18 (b) 1/12 (c) 1/13 (d) 1/6 (e) none of the foregoing

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