CAT 2008: Quantitative Questions a Day 51-100 -The discussions-Brought to you by SMOT

[medulla]

Hi Puys,

Lets assume that a plane is parallel to the length so that it divides the height H into H1
and H2 such that H = H1+H2 i.e. H1 = (H-H2)
Now the surface area after the rectangular block = 2[LH+LB+BH]
This will be equal to addition of surface areas of two new rectangular boxes.
(If this assumption is wrong everything solved below is wrong!!! )

2(LH + 100L + 100 H) = 2(LH1 + 100L + 100H1) + 2 (LH2 + 100L + 100H2)
Substitute H1 = (H-H2)
LH + 100L + 100 H = L (H-H2) + 100L + 100 (H-H2) + LH2 + 100L + 100H2
LH + 100H = LH - LH2 + 100L + 100H - 100H2 + LH2 + 100H2

100 L = 0
L = 0

Option 5) None of these...

I dont know whether this approach is correct!!!

I hope noone will groan at me for most pathetic solution ever!!!

[gripened]

Originally Posted by medulla

Hi Puys,

Lets assume that a plane is parallel to the length so that it divides the height H into H1
and H2 such that H = H1+H2 i.e. H1 = (H-H2)
Now the surface area after the rectangular block = 2[LH+LB+BH]
This will be equal to addition of surface areas of two new rectangular boxes.
(If this assumption is wrong everything solved below is wrong!!! )

2(LH + 100L + 100 H) = 2(LH1 + 100L + 100H1) + 2 (LH2 + 100L + 100H2)
Substitute H1 = (H-H2)
LH + 100L + 100 H = L (H-H2) + 100L + 100 (H-H2) + LH2 + 100L + 100H2
LH + 100H = LH - LH2 + 100L + 100H - 100H2 + LH2 + 100H2

100 L = 0
L = 0

Option 5) None of these...

I dont know whether this approach is correct!!!

I hope noone will groan at me for most pathetic solution ever!!!

Are you sure you don't want me to groan ...Just kiddin'...
I won't say much, but please try and explain as to what you think similar blocks means? And why are you trying to calculate surface area anyways? Maybe that'll help you figure as to what you are doing wrong...Just a maybe...
And yes, any attempt you make, you always step out of it a bit wiser, so don't worry about how your solution is...

[Aarav]

Originally Posted by gripened

Just a thought, are we talking of just integer solutions here ?
Because from as I see it, if not, then there are a plethora of possibilities...

Please treat this as integer (L, H).

[nbangalorekar]

Originally Posted by pavanpadekal

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Quantitative Question # 076
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Cutting a rectangular block


A rectangular block L x 100 x H, with L ≤ 100 ≤ H is cut into two non-empty parts by a plane parallel to one of the faces, so that one of the parts is similar to the original. How many possibilities are there for (L, H)?



(1) 10 (2) 12 (3) 20 (4) 24 (5) none of these

one of the child blocks is similar to the original. This means that we shud have all the 3 lengths of the child block in the same ratio as the original
i.e.: if the lengths of the child block are (l,a,h) then:
l:a:h=L:100:H
now, the plane cutting the block is parallel to one of the 3 sides.
this means that two of the sides in the original block are going to remain same & only the 3rd side will change.
since H is the max, the plane has to cut thru 'H'
now since 100 was the 2nd max value of one of the sides in parent block, it will become the 'h' (height) in the child block that is similar.{this is also bcoz we have to preserve the ratio of the sides}
now L in original block will become the 'a' in child block.

we can see that a=100/p {since ratio is conserved & in effect the ratio of child block becomes =a:L:100....... p=>integer}
EDIT:
L:100=100:H
so we get LH=10000
get factors of 100000 such that L<100..
answer comes to 12.

[Aarav]

Sorry guys, I suffer from this habit of missing "integer" word. This has happened twice this year in QQAD now. Read it completely from here.

A rectangular block L x 100 x H, where L and H are integers, with L ≤ 100 ≤ H is cut into two non-empty parts by a plane parallel to one of the faces, so that one of the parts is similar to the original. How many possibilities are there for (L, H)?

(1) 10 (2) 12 (3) 20 (4) 24 (5) none of these

[gripened]

Originally Posted by Aarav

Please treat this as integer (L, H).

Answer (2) : 12
Oh crap...Big mistake...
NOTE : Previous post edited as well...
Case iii. divide H. This is the only valid case...I don't know why but just H/2 was entering my sloshed brain...Neways, correction, no need to consider 2 cases for divide H...

We have L*H = 10000, and N = H^3/1000000...
Hence since L and H are integers, we have
L*H = (2^4)*(5^4)

Hence we just need to find valid factors...
L ________________H
5^p.2^q _______5^(4-p).2^(4-q) , 0<=p < 3, 0<=q<=4, since L <=100

Hence ,
L can take : 1,2,4,5, 8,16, 10, 20, 25, 40, 50, 80 (L=100 isn't a valid value)...

Hence 12 options...

Answer : (2) 12

[Aarav]

Originally Posted by gripened

Answer (2) : 12
Oh crap...Big mistake...

Tell me your forte and weak areas in quant. I feel you are not being enough challenged here

Waise, some of your company mates were regular in QQAD last year -> Apple (Sameer, went to IIM C), and Moiz (not into CAT), if you know them by any chance?

[Fuzon]

hi puys !
the questions are getting meaner by the day ....

by what I comprehend of similar, its this , that the ratio of leangth is to breadth is to height shd be same ---> is this thought right ?

if yes then i feel none of the combinations will give u a correct answer as 100 will always be a constant and tweaking other values wont help much and thus 'None Of these'

if No then there can be many possiblities for this logic so again 'None of these' ...

need your help ... Aarav am i right in thinking that the L:B:H ratio is same or have i completely lost it due to yesterdays Trust Vote pandemonium ?

[Aarav]

Originally Posted by Fuzon

hi puys !
the questions are getting meaner by the day ....

by what I comprehend of similar, its this , that the ratio of leangth is to breadth is to height shd be same ---> is this thought right ?

if yes then i feel none of the combinations will give u a correct answer as 100 will always be a constant and tweaking other values wont help much and thus 'None Of these'

if No then there can be many possiblities for this logic so again 'None of these' ...

need your help ... Aarav am i right in thinking that the L:B:H ratio is same or have i completely lost it due to yesterdays Trust Vote pandemonium ?

Please see this hint if it helps.

We must cut the longest edges, so the similar piece has dimensions L x 100 x K for some 1 <= k < H. The shortest edge of this piece cannot be L, so it must be k. Thus L x 100 x H and k x L x 100 are similar.

[dewan_iitr]

Hi Puys,

i am solving a problem after two days...
din had a clue abt yesterday and mondays problems...
even more tough were gripened solution...

todays problem ---

H:100:L
we can make a change only across H.

also H/100 = 100/L
so H*L = 10000 = 2^4 * 5^4

now we have to devide H such that 100 takes place of H, L takes place of 100 and new H (ie H') for L and new ratio remains same.

started with L as 1 but thats not possible.
10000:100:1 => 100:1:.01

i found these as possible ratios -

1) 1000:100:10
2) 500:100:20
3) 250:100:40
4) 200:100:50
5) 125:100:80