Quant by Arun Sharma

MBA CAT 2022
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@prsreek said:
need help on this :q) Find the remainder when 5^124 is divided 17.a) 4, b)5, c)13, d)15
5^16 = 1 mod 17 by euler thoerem
5^128 = 1 mod 17
625 N = 1 mod 17 by inverse euler
625N -1 is divisble by 17
4 will satisfy this...as 625(4) - 1 = 2499 which is 17*147
so reaminder is 4
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@prsreek said:
need help on this :q) Find the remainder when 5^124 is divided 17.a) 4, b)5, c)13, d)15
4 only
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@clearwater said:
Number Systems LOD3.43. The remainder when 2^2 + 22^2 + 222^2 + .......... (222.....49 two's)^2 is divided by 9 is?????a.2b.5c.6d.744. The sum of the digits in the multiplication N = 202 x 20002 x 2000002 x .....2(31 zeros) is???a. 112b.160c.144d.cannot be determined
43) 6
44) 160
both have been discussed in our quant section 2-3 days back.
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Can neone help me wid this problem pls..!!! time and distance pg 299. Two cyclist start simulataneously towars each other from aurangabad and ellora which are 28 km apart. an hour later they meet up and keep peadaling with the same speed without stopping. The second cyclist arrives at ellora 35 minutes later than the first arrives at aurangabad.Find the spped of the cyclist who started from ellora.

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@msabhi

This is question no. 14 in LOD 2 of Time Speed Distance chapter in Arun Sharma's Quant book:
Two indian tourists in the US cycled towards each other, one from point A and the other from point B. The first tourist left point A 6 hrs later than the second left point B, and it turned that he travelled 12 km less than the second tourist. After their meeting, they kept cycling with the same speed, and the first tourist arrived at B 8 hours later and the second arrived at A 9 hours later. Find the speed of the faster tourist.
(a) 4 km/hr
(b) 6 km/hr
(c) 9 km/hr
(d) 2 km/hr
(e) 5 km/hr

Bhai can u pls xplain how to solve this problem.. gettin stuck all d tym... 😐
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Can someone pls solve this question:(Arun Sharma,5th edition, Pg68)

QThe remainder when 2^2 + 22 ^2+222^2+2222^2+.......(222....49 twos)^2 is divided by 9 is: a)2 b)5 c)6 d)7
Kindly explain the answer.
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@ThankYou said:
Can someone pls solve this questionArun Sharma,5th edition, Pg68)QThe remainder when 2^2 + 22 ^2+222^2+2222^2+.......(222....49 twos)^2 is divided by 9 is: a)2 b)5 c)6 d)7Kindly explain the answer.
2^2(1^2+11^2+....+(11..49times)^2)
2^2[(1^2+2^2+3^2+....+9^2)*5 + 1^2 + 2^2+3^2+4^2]
2^2[0+1+4+0+7]
4*3=3

do u have the correct options?
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@ThankYou c). 6

Tell me if the answer is right , then i will tell u the solution.

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A magazine company prints 5000 copies at 5,00,000 every month.In July,they distribute 500 free copies.Besides they were able to sell 2/3rds of the remaining magazines at 20% discount.Besides the remaining magazines were sold at the printed price of Rs 200.Find the percentage profit for the magazine company(assume a uniform 20% of the sale price as the vendor's discount and assume no other source of income).

A.56
B.24.8
C.28.5
D.22.6

Correct Answer is 24.8. I wanted to know the procedure.

Thanks in advance.
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@Subhashdec2 said:
2^2(1^2+11^2+....+(11..49times)^2)2^2[(1^2+2^2+3^2+....+9^2)*5 + 1^2 + 2^2+3^2+4^2]2^2[0+1+4+0+7]4*3=3do u have the correct options?
@Subhashdec2
Yes, I wrote the correct options...
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@nikhilaka_jason said:
@ThankYou c). 6Tell me if the answer is right , then i will tell u the solution.
@nikhilaka_jason
Yes, thats the right answer. Pls explain
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Another question from arun Sharma book...

Q. 25 sets of problems on DI one for the DI section of 25 tests were prepared by research team. DI section of each test consisted of 50 ques of which 35 were unique, i.e they had not been used in the other 24 tests. What could b the max possible no. of ques. prepared for DI sections of all 25 tests put together?
a)1100 b)975 c)1070 d)1055
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can someone please give me the complete solution to this sum
Water running in a cylindrical pipe of inner diameter 7 cm is collected in a container@ 192.5 liters/min.find the rate of flow of water. use pi=22/7.
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@shov2210 area * rate of flow = volume of flow per min..so rate of flow = (192.5*.001/60) / (22/7 * 7/2 * 7/2)=watever the ans comes out 😛 :P
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Please guyz help me out with this one from Number systems:

Q. A triangular number is defined as a number which has the property of being expressed as a sum of consecutive nos starting with 1. How many triangular nos less than 1000 have a property that they are difference of squares of 2 consecutive natural nos.??

Choices: a) 20; b)21 ; c)22 ; d)23

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Difference between any two consecutive squares is always odd, so we need to look for all those triangular numbers which are odd.


Triangular numbers can be written as n(n + 1)/2 and its less than 1000, so n(n + 1)/2
=> n ‰¤ 44

We know that one of n and (n + 1) will always be odd
Since n(n + 1)/2 is odd we can say that the even number of the two should be of form 4k + 2

So, n = 4k + 2 (11 cases less than 45)
when n + 1 = 4k + 2
=> n = 4k + 1 (11 cases less than 45)

So, 22 such numbers
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@maanas.vyas said:
Please guyz help me out with this one from Number systems:Q. A triangular number is defined as a number which has the property of being expressed as a sum of consecutive nos starting with 1. How many triangular nos less than 1000 have a property that they are difference of squares of 2 consecutive natural nos.??Choices: a) 20; b)21 ; c)22 ; d)23
total number of no. which can be expressed as a sum of numbers starting from 1 = 44 as 44*45/2 = 22*45 = 990
among this 44 numbers , we have to find numbers which can be expressed in the form of n^2 - (n-1)^2 = 2n -1
any odd number can be expressed so..
hence 22 such numbers..
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@maanas.vyas said:
Please guyz help me out with this one from Number systems:Q. A triangular number is defined as a number which has the property of being expressed as a sum of consecutive nos starting with 1. How many triangular nos less than 1000 have a property that they are difference of squares of 2 consecutive natural nos.??Choices: a) 20; b)21 ; c)22 ; d)23
22
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@catahead I think that the answer should be 21 as the first triangular number i.e. 1 can't be expressed as a difference of squares of two consecutive NATURAL numbers.
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@kittu12 answer cannot be determined as there is insufficient data. And 126 kg is not price but its quantity .