1. What is the next number of the following sequence
3 × 7 = 21
7 × 11 = 77
11 × 15 = 165
15 × 19 = 285
19 × 23 = 437 ans
T(n) = (4n – 1) × (4n + 3)
Put value of n find any term.
2. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Just go in reverse order.
Check the options with th subtracting 18 from each option for getting reverse number.
42 – 18 = 24 (which is in reverse).
So answer is 24
3. Two guys work at some speed. After some time one guy realises he has done only half of the other guy completed which is equal to half of what is left So how much faster than the other is this guy supposed to do to finish with the first.
If x is the part of task this is completed then,
1st has done work = (1 – x)/4 and 2nd has done work = (1– x)/2
So 2nd will have to increase his speed by 2 times.
4. We are given 100 pieces of a puzzle. If fixing two components together is counted as 1 move ( a component can be one piece or an already fixed set of pieces), how many moves do we need to fix the entire puzzle.
Fixing 2 components together = 1 move
98 components are left ,to again fix one of these to the other two = 1 move
97 comp left,so 97 more moves
Total = 1 + 1 + 97 = 99.
5. The ime a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?
Answer: 3 : 1
Speed of freight train = x
Speed of passenger train = y
Sum of their length = s
So time = s/(x – y)when both are in same direction
Time = s/(x + y) when opposite direction
From question s/(x – y) = 2.s/(x + y) so solving this we get, x/y = 3/1.
So x : y = 3 : 1
6. At a recent birthday party there were four mothers and their children. Aged 1,2,3 and 4. from the clues below can you work out whose child is whose and their relevant ages?
- It was jane's child's birthday party.
- Brian is not the oldest child.
- Sarah had Anne just over a year ago.
- Laura's Child will be next birthday.
- Daniel is older than Charlie is.
- Teresa's child is the oldest.
- Charlie is older than Laura's child.
According to given points.
Anne is one yr old her mother is Sarah
Brian is 2 yr old his mom is Laura
Charlie is 3 yr old his mom is Jane
Daniel is 4 yr old his mom is Teresa.
And its charlie's birthday party.7. Ajith was driving down the country side when he saw a farmer tending his pigs and ducks in his yard. Ajith asked the farmer how many of each he had. The farmer replied that there were 60 eyes and 86 feet between them. How many ducks and how many pigs were there ?
Let the no of ducks be x and no of pigs be y.
Then,since there are 60 eyes in total and both ducks and pigs have 2 eyes we have 2x + 2y = 60 - - - (1)
And total number of legs are 86, ducks have 2 legs while a pig has four so 2x + 4y = 86 - - - (2)
Subtracting (1) from (2) ,we get
2y = 26. ie. y = 13
Putting value in - - - (1),
We get x = 17
8. A supportive young hare and tortoise raced in opposite directions around a circular track that was 100 yards in diameter. They started at the same spot, but the hare did not move until the tortoise had a start of one eighth of the distance ( that is, the circumference of the circle). The hare held such a poor opinion of the other’s racing ability that he sauntered along, nibbling the grass until he met the tortoise. At this point the hare had gone one sixth of the distance. How many times faster than he went before must the hare now run in order to win the race ?
Answer: more than 5 times
The hare and the tortoise are at the same point when hare have to cover 5/6 of the distance and tortoise have to cover 1/6 of the distance to complete the race.
If x is the speed of tortoise then it'll take 1/(6 x) time to finish.
So, hare will have to run more then 5 times the speed of tortoise to win the race.
9. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Let numbers are n,n + 2,n + 4
Now 3 n = 2(n + 4) + 3
3 n – 2 n = 11
N = 11 then consecutive odd numbers are 11, 13, 15
10. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A. 12 days
B. 15 days
C. 16 days
D. 18 days
Work done in 3 days = (3/20) + (1/30) + (1/60) = 1/5
Remaining work = 4/5
If 1/5 work is done in 3 days then,
4/5 work is done in (3 × 5 × 4)/5 = 12 days
Total no. of days will become 12+3=15 days for the complete work to be done