Official Quant thread for CAT 2013

MBA CAT 2022
2301
@Torque024 said:
AB^2+BC^2=3 AB^2+(2*BD)^2=3 -----eq 1 Sin 60 = AB/AC AB= Sin60*Sqrt(3) From AB we can find BD from eq 1 AD= AB^2+ BD^2
draw a perpendicular bisector to BC, now i want to put the point D on this , i can put it anywhere, say 9^9999 units away, so length of AD will depend upon my choice of placement of D, since, BD is not given AD cannot be determined
2302
@sauravd2001 said:
@krum bhai maien toh bc ke bich mein liya hai toh us hisab se calculate kar diya
me too!! in the exam as well...
2303
@albiesriram bhai answere tu hi bta de?
2304
@realslimshady said:
how many squares between 1 and 1000 (both inclusive) can be expressed as the diff. of the squares of 2 non negative integers. A.750 B. 748 C.300 D.250 please show approach as well.
case1:(x2-y2)=(x+y)(x-y)
suppose when one is even and other is odd OR when both are odd then product will be odd so all the odd numbers can be written in this form=>500
case:when both x and y are even the x2-y2 will be of form 4n so total number of this form will be 250
total cases =750
2305

i dont have OA. I have just given the test.!

bhaiyon please discuss question 1 of mine briefly..That treee wala question.
2306
@realslimshady said:
how many squares between 1 and 1000 (both inclusive) can be expressed as the diff. of the squares of 2 non negative integers. A.750 B. 748 C.300 D.250 please show approach as well.
every natural number can be expressed as difference of squares of 2 +ve numbers except for the multiples of 4

so total = 1000-1000/4=750
2307
@realslimshady said:
how many squares between 1 and 1000 (both inclusive) can be expressed as the diff. of the squares of 2 non negative integers. A.750 B. 748 C.300 D.250 please show approach as well.
750

as a^2 -b^2 = N
(a-b) (a+b) = N
now a,b both has to be either even or both odd..cant be one even and one odd...
as in tha case wont get the integer..
ie all cases except 4n+2
2308

Chalo guys GN, hath garam karnae ka tym aa gaya. Byee

2309
@krum said:
every natural number can be expressed as difference of squares of 2 +ve numbers except for the multiples of 4so total = 1000-1000/4=750
8 can be exressed as 3-1. 3+1
2310
@milestogo3 i too was thinking the same
2311
@milestogo3 said:
8 can be exressed as 3-1. 3+1
3 is not a sq of a natural no
2312
On a straight line, five points are located. You choose any two points and note down the distance between them. The ten distances so obtained are written down in an increasing order as follows: 2, 4, 5, 7, 8, n, 13, 15, 17 19. What is the value of n?
2313
@Subhashdec2 said:
3 is not a sq of a natural no
a^2-b^2 = a-b . a+b = 8

>4 4n+2 no of cases exclude..
2314

happy diwali to all :)))))))))


______/\_____

2315
Pia and Ria simultaneously started running from point A towards point B at a distance of 10 km on a linear track. Pia on reaching point B, took a rest for 30 minutes, turned back and started running towards point A. Ria on reaching point B, immediately turned back and started running towards point A. Both of them reached point A simultaneously. If the difference between their speeds is 2 kmph, in how much time will Ria cover a distance of 24 km?

A) 3 hours
B)2.4 hours
C)2 hours
D)3.5 hours

If anyone knows how to solve this question without using equation will be welcomed...
2316
@pankaj1988 said:
On a straight line, five points are located. You choose any two points and note down the distance between them. The ten distances so obtained are written down in an increasing order as follows: 2, 4, 5, 7, 8, n, 13, 15, 17 19. What is the value of n?
12?
2317
@dipz10 said:
Pia and Ria simultaneously started running from point A towards point B at a distance of 10 km on a linear track. Pia on reaching point B, took a rest for 30 minutes, turned back and started running towards point A. Ria on reaching point B, immediately turned back and started running towards point A. Both of them reached point A simultaneously. If the difference between their speeds is 2 kmph, in how much time will Ria cover a distance of 24 km?A) 3 hoursB)2.4 hoursC)2 hoursD)3.5 hoursIf anyone knows how to solve this question without using equation will be welcomed...
is it 3 hrs???????

2318
@dipz10 said:
Pia and Ria simultaneously started running from point A towards point B at a distance of 10 km on a linear track. Pia on reaching point B, took a rest for 30 minutes, turned back and started running towards point A. Ria on reaching point B, immediately turned back and started running towards point A. Both of them reached point A simultaneously. If the difference between their speeds is 2 kmph, in how much time will Ria cover a distance of 24 km?A) 3 hoursB)2.4 hoursC)2 hoursD)3.5 hoursIf anyone knows how to solve this question without using equation will be welcomed...
Go through the options..start with option (a)..if Ria covers 24km in 3 hours..her speed must be 8 kmph
hence, speed of pia = 10 or 6
consider her speed to be 10
pia covers distance between a and b in an hour..but she also rests for half an hour
by this time ria has covered 8+4 = 12km
So she is 2km ahead of pia. Now, pia starts running again..and completes 10km in an hour, while ria completes 8km in an hour.
So they reach simultaneously..
So the answer is option (A)
2319
@dipz10 said:
Pia and Ria simultaneously started running from point A towards point B at a distance of 10 km on a linear track. Pia on reaching point B, took a rest for 30 minutes, turned back and started running towards point A. Ria on reaching point B, immediately turned back and started running towards point A. Both of them reached point A simultaneously. If the difference between their speeds is 2 kmph, in how much time will Ria cover a distance of 24 km?A) 3 hoursB)2.4 hoursC)2 hoursD)3.5 hoursIf anyone knows how to solve this question without using equation will be welcomed...
let speed be v and v+2

20/v=20/v+2 + 1/2
v=8

hence 24/8=3
2320
@dipz10 said:
Pia and Ria simultaneously started running from point A towards point B at a distance of 10 km on a linear track. Pia on reaching point B, took a rest for 30 minutes, turned back and started running towards point A. Ria on reaching point B, immediately turned back and started running towards point A. Both of them reached point A simultaneously. If the difference between their speeds is 2 kmph, in how much time will Ria cover a distance of 24 km?A) 3 hoursB)2.4 hoursC)2 hoursD)3.5 hoursIf anyone knows how to solve this question without using equation will be welcomed...
3 hrs...approach through eq. only