Last 2 digits of N are 38 and there are 3 factors between root(N) and 1. Then what is the number of factors of N.
Ans: (2) 8 Solutions 3 factors between 1 and root(N), hence 4 are less than root(N) so 4 are greater than N. and N is not a perfect square because last digit cannot be 8 for a perfect square. Hence total There 8 factors for N.
You are blindfolded and given a deck of cards in which exactly 16 cards are facing up. You have to divide it into 2 piles having exactly same number of cards facing up. How would you do it.
Solution make 2 decks. 36 cards and 16 cards. ( x cards in 36 deck and 16-x cards in 16 deck are facing up) Now reverse the deck of 16 cards, so now it also has x cards facing up.
2N has 2f factors and 6N has 3f factors, then which of the following can be the value of N
Answer: (2) 1593 Solution: 2N has 2f means N is not divisible by 2. and 6N has 3f factors means factor has become 1.5 times that is 3/2 times. It means when multiplied by 3 factor become 2f to 3f. Hence power of 3 became 1 to 2. Hence N is divisible by 3. Only option that is divisible by 3 and not by 2 is option(2).
An egg when thrown from a particular floor of a 10 story building get broken, but will not break if thrown from any floor below that. You have 2 eggs to find out that particular floor. What is the minimum number of attempts to ensure the floor from which the egg breaks.
Answer: 4 attempts Solution: First throw from floor number 4 Breaks: then 3 more attempts needed (total 4 attempts) if it doesn’t break, then throw from floor number 7 Breaks: then 2 more attempts needed (total 4 attempts) If not then throw floor number 9.
how many integer solutions does (4n+19)/(n-3) has?
2
4
8
infinte many
Answer: (2) 4 solutions
Solution
(4n-12+31)/(n-3) = 4+31/(n-3)
so now 31/(n-3) let’s say equal to 31/x should be integer
it will be integer when x is a factor of 31 (both positive and negative)
there are 2 positive factors of 31 and 2 negative factors. Hence total 4 solutions.
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With how many bearers can an explorer can an explorer make a six day march across an absolutely barren desert if he and the available bearers can each carry only enough food and water to last one man four days ?
Solution with 2 bearers. One bearer will return after one day, giving his extra 2 supplies to explorer and other bearer, and second bearer will return next day.
A shopkeeper cheats 30% while buying and cheats 15% while selling and does transaction at cost price.
Find shopkeepers profit percentage
Solution shopkeeper pays for 100gm and takes 130gms while buying. and then shopkeer covers the money of 100 gm while selling 85 gms. effectively in the whole transaction shopkeeper recovers his entire cost by selling only 85 gms. So he is still left with 45 gms. so now the amount he gets by selling 45 gms would be his profit over his spending. (his spending is equal to the amount he gets by selling 85 gms) 45 gms is his profit over 85 gms profit % = (45/85)*100 = 53%
In a game show host asks you select 1 of the 3 doors. behind one of the doors is a car and other two are empty. In the show after you select the door hosts opens an empty door, then further asks you if you want to stick to your original choice or you want to switch. What would you do and why?
Solution one must switch to increase his probability of winning. Because initially let’s consider 3 cases You select different doors in different cases door-1 (nothing), the host opens door-2, if you switch you win door-2 (nothing), the host opens door-1, if you switch you win door-3 (car), the host opens either door 1 or 2, if you switch you lose So from above, it is clear that if you switch you win 2 out 3 cases. but if you stick to your original choice you will win only 1 out of 3 cases.
