Official Quant thread for CAT 2013

MBA CAT 2024
8741
@anytomdickandhary said:
what is the smallest pythagorean triplet (i.e a+b+c is minimum) s.t all of a,b,c are perfect squares?ATDH.

This would give a^4 +b^4 = c^4....but at this point Monsieur Fermat would object....and hence I guess no integral solution?

regards
scrabbler
8742

A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?

8743
@veertamizhan said:
A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?
12:20?

regards
scrabbler
8744
@scrabbler I know right? the books says 12:40 pm
8745
@veertamizhan said:
@scrabbler I know right? the books says 12:40 pm
M also getting 12:20
8746
@veertamizhan said:
A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?
(30/60)Sc+(30/60)Sa=(11-9)(Sc-Sa); Distance AB=(11-9)Sc
Sc/Sa=25/15
Ta=AB/Sa=2Sc/Sa = 50/15=3:20
Time=9+3:20=12:20
8747
@veertamizhan said:
A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?
let AB=x
since car takes 2hrs from A to B and half an hour from B to C ,
then BC =x/4
implies CA=3x/4
now auto takes 150 min to travel A to C ,implies it will take 50 min from C to B
therefore time at which auto will reach B = 11:30 +(50min)= 12:20
8748
@veertamizhan said:
A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?
Time is coming out to be 3 1/3 hours
Hence time when auto reaches is 12:20 pm
8749
@veertamizhan said:
@scrabbler I know right? the books says 12:40 pm
Books are frequently wrong alas 😞

(So am I, but I can at least be convinced by good logical reasons ;)

My reasoning - the speeds are in the ratio 5 : 3 (as the distances covered till their meeting are in that ratio) and so the times for a full lap also should be the same. The car took 2 hours or 120 min so the auto should take 200 min which is 3 hr 20 min which implies 12:20.

regards
scrabbler
8750
@veertamizhan said:
A car overtakes an auto at point A at 9 am. The car reaches pont B at 11 am and immediately turns back. It again meets the auto at point C at 11:30 am. At what time will the auto reach B?
12.20 pm

Time taken by auto to travel from A to C = 2.5 hours
Time taken by car to travel from A to B = 2 hours
Time taken by car to travel from B to C = 0.5 hours
So time taken by car to travel from A to C = 1.5 hours

So time taken by auto to travel from C to B = 2.5*0.5/1.5 = 50 minutes

11.30 + 00.50 = 12.20 pm
8751
A trader has bought some goods at a discount of 20% on the list price. He wants to mark them at
such a price that even if he gives a discount of 20% on the marked price he still makes a profit of
25%. If he marks the goods by 20% points more than the proposed price and allows a discount of
50%, then what will be the profit / loss percentage?
(1) 27.5% profit (2) 30% loss (3) 27.5% loss (4) 30% profit (5) None of these
8752
@sujamait said:
a right angled triangle with longest side 80,construct 3 paths from the corner point opposite to the longest side such that these three paths divide the longest side into four equal segments.determine the sum of the lengths of three paths.
8753
@Cat.Aspirant123 said:
A trader has bought some goods at a discount of 20% on the list price. He wants to mark them atsuch a price that even if he gives a discount of 20% on the marked price he still makes a profit of25%. If he marks the goods by 20% points more than the proposed price and allows a discount of50%, then what will be the profit / loss percentage?(1) 27.5% profit (2) 30% loss (3) 27.5% loss (4) 30% profit (5) None of these
NOT?
L.P at which he buys= 80(assume)
S.P=100 (25% PROFIT)
M.P=125

NOW, 20% INCREASE IN M.P= 150
Discount-= 50%= 75
S.P=75, Hence loss of 5 rs.
5/80*100= 6.25% loss
8754
@Cat.Aspirant123 said:
A trader has bought some goods at a discount of 20% on the list price. He wants to mark them atsuch a price that even if he gives a discount of 20% on the marked price he still makes a profit of25%. If he marks the goods by 20% points more than the proposed price and allows a discount of50%, then what will be the profit / loss percentage?(1) 27.5% profit (2) 30% loss (3) 27.5% loss (4) 30% profit (5) None of these
None of these

8755
@htomar said:
None of these
nope
8756
@pyashraj said:
@Cat.Aspirant123None of these hai kya?? 40% Loss ...
no oa s diff
8757
@pratyush9811 said:
NOT?L.P at which he buys= 80(assume) S.P=100 (25% PROFIT)M.P=125NOW, 20% INCREASE IN M.P= 150Discount-= 50%= 75S.P=75, Hence loss of 5 rs.5/80*100= 6.25% loss
i also got 6.25 but oa they have given is 27.5 i think its there printing mistake
8758
@Cat.Aspirant123 said:
i also got 6.25 but oa they have given is 27.5 i think its there printing mistake
Yep..has to be a printing mistake.
8759
@Cat.Aspirant123 said:
i also got 6.25 but oa they have given is 27.5 i think its there printing mistake

Also got 6.25. Galat hoga.

regards
scrabbler
8760
@Cat.Aspirant123 said:
i also got 6.25 but oa they have given is 27.5 i think its there printing mistake
It has to be printing mistake