<![CDATA[Quant Boosters - Maneesh - Set 1]]>Number of Questions - 30
Topic - Quant Mixed Bag
Solved ? - Yes
Source -
]]>https://www.mbatious.com/topic/1017/quant-boosters-maneesh-set-1RSS for NodeWed, 23 Oct 2019 11:39:15 GMTThu, 14 Dec 2017 09:16:46 GMT60<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:16:46 GMT]]>Number of Questions - 30
Topic - Quant Mixed Bag
Solved ? - Yes
Source -
]]>https://www.mbatious.com/post/9584https://www.mbatious.com/post/9584Thu, 14 Dec 2017 09:16:46 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:17:39 GMT]]>Q1) N = 2^3 * 3^4 * 5^9
Find the product of all factors of N which are not divisible by 12
]]>https://www.mbatious.com/post/9585https://www.mbatious.com/post/9585Thu, 14 Dec 2017 09:17:39 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:18:22 GMT]]>Number of factors = 4 * 5 * 10 = 200
Product of factors = 2^300 * 3^400 * 5^900
Number of factors which are divisible by 12 = 2 * 4 * 10 = 80
Product of factors which are divisible by 12 = 2^40 * 3^120 * 5^360 * 12^80
Required product = 2^300 * 3^400 *5^900 / 2^40 * 3^120 * 5^360 * 2^160 *3^80
= 2^100 * 3^200 * 5^540
]]>https://www.mbatious.com/post/9586https://www.mbatious.com/post/9586Thu, 14 Dec 2017 09:18:22 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:19:21 GMT]]>Q2) N = 2^15 * 3^12 How many factors of N^2 are less than N but do not divide N completely?
]]>https://www.mbatious.com/post/9587https://www.mbatious.com/post/9587Thu, 14 Dec 2017 09:19:21 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:19:41 GMT]]>Factors of N = 16 * 13 = 208
Factors of N less than N = 208 - 1 = 207
Factors of N^2 = 31 * 25 = 775
Factors of N^2 less than N = (775 - 1)/2 = 387
So ans = 387 – 207 = 180
]]>https://www.mbatious.com/post/9588https://www.mbatious.com/post/9588Thu, 14 Dec 2017 09:19:41 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:23:39 GMT]]>Q3) The numbers 2604,1020 and 4812 when divided by a number N give the same remainder of 12. Find the highest such number N
]]>https://www.mbatious.com/post/9589https://www.mbatious.com/post/9589Thu, 14 Dec 2017 09:23:39 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:24:00 GMT]]>Since all the numbers are giving remainder 12, (2604-12),(1020-12),(4812-12) are multiples of N
2592, 1008, 4800
So N will be HCF of 2592,1008 and 4800
2592 = 2^5 * 3^4
1008 = 2^4 * 7 * 3^2
4800 = 2^6 * 5^2 * 3
HCF = 2^4 * 3 = 48
]]>https://www.mbatious.com/post/9590https://www.mbatious.com/post/9590Thu, 14 Dec 2017 09:24:00 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:24:13 GMT]]>Q4) The numbers 400,536 and 645 when divided by a number N gave remainders of 22,23 and 24 respectively.Find the greatest such number N
]]>https://www.mbatious.com/post/9591https://www.mbatious.com/post/9591Thu, 14 Dec 2017 09:24:13 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:24:28 GMT]]>N will be the HCF of (400-22),(536-23) and (645-24)
HCF(378,513,621) = 27
]]>https://www.mbatious.com/post/9592https://www.mbatious.com/post/9592Thu, 14 Dec 2017 09:24:28 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:24:52 GMT]]>Q5) The HCF of two numbers is 12 and their sum is 288. How many pairs of such numbers are possible?
]]>https://www.mbatious.com/post/9593https://www.mbatious.com/post/9593Thu, 14 Dec 2017 09:24:52 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:25:08 GMT]]>Let numbers be 12a, 12b
12(a+b) = 288
a+b = 24 and a and b are co prime
Hence(1,23)(5,19)(7,17)(11,13)
Hence 4 pairs available.
]]>https://www.mbatious.com/post/9594https://www.mbatious.com/post/9594Thu, 14 Dec 2017 09:25:08 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:29:47 GMT]]>Q6) HCF of 2 numbers are 12 and their product is 31104. How many such numbers are possible?
]]>https://www.mbatious.com/post/9595https://www.mbatious.com/post/9595Thu, 14 Dec 2017 09:29:47 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:29:59 GMT]]>Let numbers are 12a n 12b
144ab = 31104
ab = 216
a and b are coprime
(1,216)(8,2)
Only two pairs possible.
]]>https://www.mbatious.com/post/9596https://www.mbatious.com/post/9596Thu, 14 Dec 2017 09:29:59 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:30:34 GMT]]>Q7) Find the Highest five digit number that is divisible by each of the numbers 24, 36, 45 and 60?
]]>https://www.mbatious.com/post/9597https://www.mbatious.com/post/9597Thu, 14 Dec 2017 09:30:34 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:30:48 GMT]]>LCM (24,36,45,60) => 24 = 2^3 * 3
36 = 3^2 * 2^2
45 = 3^2 * 5
60 = 2^2 * 3 * 5
LCM = 2^3 * 3^2 * 5 = 360
So we have to find highest five digit multiple of 360
99999 mod 360 = 279
so answer 99999-279 = 99720
]]>https://www.mbatious.com/post/9598https://www.mbatious.com/post/9598Thu, 14 Dec 2017 09:30:48 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:31:18 GMT]]>Q8) Find the lowest number which gives a remainder of 5 when divided by any of the numbers 6, 7, 8 ?
]]>https://www.mbatious.com/post/9599https://www.mbatious.com/post/9599Thu, 14 Dec 2017 09:31:18 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:31:39 GMT]]>LCM(6, 7, 8) = 168
number = 168 + 5 = 173
]]>https://www.mbatious.com/post/9600https://www.mbatious.com/post/9600Thu, 14 Dec 2017 09:31:39 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:32:02 GMT]]>Q9) What is the smallest number which when divided by 9,18 and 24 which leaves a remainder of 5, 14 and 20 respectively
]]>https://www.mbatious.com/post/9601https://www.mbatious.com/post/9601Thu, 14 Dec 2017 09:32:02 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Fri, 15 Dec 2017 04:21:41 GMT]]>Q10) In a book store “OM INNOVATIVE BOOK STORE“ is flashed using neon lights. The words are individually flashed at intervals of 8/3, 16/3 , 14/3 and 15/2 seconds respectively and each word is put off after a second. The least time after which the full name of the book store can be read for a second?
]]>https://www.mbatious.com/post/9602https://www.mbatious.com/post/9602Fri, 15 Dec 2017 04:21:41 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:32:47 GMT]]>Q11) A number when divided by 3, 4, 5 and 6 always leave a remainder 2, but leaves no remainder when divided by 7. What is the lowest such number possible?
]]>https://www.mbatious.com/post/9603https://www.mbatious.com/post/9603Thu, 14 Dec 2017 09:32:47 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:32:59 GMT]]>LCM(3, 4, 5, 6) = 60
Number of the form 60a + 2
60a + 2 = 7b
lowest such number -> 182 when a = 3 & b = 26
]]>https://www.mbatious.com/post/9604https://www.mbatious.com/post/9604Thu, 14 Dec 2017 09:32:59 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:33:20 GMT]]>Q12) For how many pairs (a,b) of natural numbers is the LCM of a and b 2^3 * 5^7 * 11^13?
]]>https://www.mbatious.com/post/9605https://www.mbatious.com/post/9605Thu, 14 Dec 2017 09:33:20 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:33:40 GMT]]>Let one of the number contains 2^3
Other may contain 2^0,2^1,2^2,2^3 -> 4 possibilities
Number of ordered pairs -> 2 * 4 – 1 = 7 (since (2^3,2^3) required only once)
Similarly powers of 5 -> 2 * 8 – 1 = 15
Powers of 11-> 2 * 14 – 1 = 27
Total 7 * 15 * 27 = 2835
]]>https://www.mbatious.com/post/9606https://www.mbatious.com/post/9606Thu, 14 Dec 2017 09:33:40 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:37:45 GMT]]>Q13) An Egyptian fraction has a numerator equal to 1 and its denominator is a positive integer. What is the maximum number of Egyptian fractions such that their sum is equal to 1 and their denominators are equal to 10 or less?
]]>https://www.mbatious.com/post/9607https://www.mbatious.com/post/9607Thu, 14 Dec 2017 09:37:45 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:38:10 GMT]]>Possible numbers 1/2 ,1/3,1/4,1/5,1/6,1/7,1/8,1/9
Out of which 1/5, 1/10, 1/7, 1/9 can be eliminated since it wont give sum of 1
Similarly 1/4 and 1/8 can be eliminated.
So remaining 1/2, 1/3 and 1/6 = > 1/2 + 1/3 + 1/6 = 1
So maximum number -> 3
]]>https://www.mbatious.com/post/9608https://www.mbatious.com/post/9608Thu, 14 Dec 2017 09:38:10 GMT<![CDATA[Reply to Quant Boosters - Maneesh - Set 1 on Thu, 14 Dec 2017 09:38:35 GMT]]>Q14) What is the minimum number of square marble tiles required to tile a floor of length 2 meters 56 cm and width 3 m and 36 cm ?
]]>https://www.mbatious.com/post/9609https://www.mbatious.com/post/9609Thu, 14 Dec 2017 09:38:35 GMT