Q11. Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up. The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month ?
A month ago it was $27 and now it is $45, a difference of $18 for a box. And 27 boxes are to be bought. The amount he would have paid more than previous month
= 27 x 18 = 486
Q12. A lady has fine gloves and hats of different colors in her closet 18 blue, 32 red and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each color ?
It is not given that how many of these items are gloves and how many are hats, if we consider that all the items are gloves then according to my opinion 32+25+2 = 59 gloves, she must take out to make sure she has a pair of each color.
Q13. A number plate can be formed with two alphabets followed by two digits with no repetition. How many possible combinations can we get ?
Q14. There are 20 persons sitting in a circle. In that, there are 18 men and 2 sisters. How many arrangements are possible, in which the two sisters are always separated by a man ?
a) 18! * 2
c) 17! * 2
In a group, assume 1 man along with two groups. So, they can be arranged in 17! ways as circular. Also, we have 18 options for choosing one man.
Same way, two sisters can be arranged in 2 ways :
making it 18! * 2
Q15. Average marks of a,b,c is 48. When d joins average becomes 47. e has 3 more marks than d. Average marks of b,c,d,e is 48. What is the marks of a ?
a + b + c = 144 (48*3)
a + b + c + d = 188
d = 44
e = 47
b + c + d + e = 192
b + c = 101
b = 43
Q16. In how many ways a team of 11 must be selected a team 5 men and 11 women such that the team must comprise of not more than 3 men.
d) None of these
The team may consist of:-
0 men + 11 women
1 men + 10 women
2 men + 9 women
or 3 men + 8 women.
So Number of ways are = 11C11+5C1 * 11C10 + 5C2*11C9+5C3*11C8 = 2256 ways.
Q17. A alone can do 1/4th of the work in 2 days. B alone can do 2/3th of the work in 4 days. If all the three work together, they can complete it in 3 days so what part of the work will be completed by C in 2 days ?
d) None of these
A can do the total work in : 8 days
B can do it in 6 days.
Let the total work be 24 units.
A = 24/8 = 3,
B = 24/6 = 4,
A + B + C = 24/3 = 8
So C = 1 unit.
In two days C will do 2 units which is 2/24th part of the total work. So 1/12th part.
Q18. The letters in the word “PLACES” are permuted in all possible ways and arranged in the alphabetical order. Find the word at 48 position.
Arranging in alphabetical order A, C, E, L, P, S
A _ _ _ _ _= 5! = 120 (more than 48)
A C _ _ _ _= 4! = 24
A E _ _ _ _= 4! = 24 (the remaining 4 letters can be arranged in 4! ways)
24+24=48 (we get the required number)
48 is the last word then as per dictionary the word will be AESPLC
Q19. An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed ?
She will have to increase her speed by 33.333% to run the same distance in 3/4s of the time hence 0.33 is the answer
Q20. A car manufacturer produces only red and blue models which come out of the final testing area completely at random. What are the odds that 5 consecutive cars of the same color will come through the test area at a time?
a) 1 in 16
b) 1 in 12
c) 1 in 32
d) 1 in 25
The odds that five consecutive cars of red color= 1/2*1/2*1/2*1/2*1/2=1/32
The odds that five consecutive cars of blue color= 1/2*1/2*1/2*1/2*1/2=1/32
The odds that five consecutive cars of same color = 1/32 + 1/32 = 1/16