divelab/Sys2Bench huggingface dataset:
Question: which one is odd?
4377
3954
9865
8454
9831
Options:
A)4377
B)3954
C)9865
D)8454
E)None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9865 is 28
Answer: C
Question: Two trains of equal length, running with the speeds of 60 and 40 kmph, take 55 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Options:
A)10 sec
B)16 sec
C)13 sec
D)67 sec
E)11 sec
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 55
D = 55 * 100/18 = 2750/9
RS = 60 + 40 = 100 * 5/18
T = 2750/9 * 18/500 = 11 sec
Answer: E
Answer: E
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
Options:
A)$1.75
B)$1.85
C)$2.00
D)$2.15
E)$2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $8.25 (a 15-cent increment) and the the difference in sequential prices of the pots is 15 cents, the largest pot PROBABLY has a price that is a 15-cent increment. From the answer choices, I would then TEST Answer A first
IF....
The largest pot = $1.75
1
1.15
1.3
1.45
1.6
1.75
Total = $8.25
So this MUST be the answer.
A
Answer: A
Question: S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is
Options:
A)198
B)297
C)320
D)402
E)405
Rationale: last term =first term +(total no. of terms-1)consecutive difference
S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is
first term = 68 ; total terms =64 ; difference = 4
68+(63)4 = 320
Ans C
Answer: C
Question: Ajay buys 6 dozen eggs for Rs 10.80, and 12 eggs are found rotten and the rest are sold at 5 eggs per rupee. Find his percentage gain or loss.
Options:
A)11 1/9 % gain
B)11 1/9 % loss
C)9 1/11 % gain
D)9 1/11 % loss
E)None of these
Rationale: 6 dozen egg cost = Rs 10.80
Since one dozen is rotten , he sells 5 dozen at 5 eggs per rupee.
Hence, S.P = Rs 12
Thus, Gain % = [(12 - 10.8) / 10.8] x 100 = 11 1/9%
ANSWER:A
Answer: A
Question: Given that there are 11 cricket players per team, how many ways can you select 3 cricket players from 4 teams if no more than one player can be selected from each team?
Options:
A)500
B)484
C)396
D)656
E)336
Rationale: First select 3 group out of available 4 groups. This cane be done in 4C3 ways = 4 ways
Now from each group we have to select one person only: 11C1 * 11C1= 11 * 11 = 121
Total ways: 121 * 4 = 484 ways.
Answer is B
Answer: B
Question: |-5| (|-20|-|4|)= ??
Source: Preparation Material MBA Center
Options:
A)64
B)–60
C)44
D)75
E)100
Rationale: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-5| = 5, |-20| = 20, and |4| = 4. Getting rid of our absolute values we have:
|-5| (|-20|-|4|) = (5) (20 - 4) = 4*16 = 64
Answer: A
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150metres
B)157m
C)750m
D)850m
E)350m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A:
Answer: A
Question: The markup on a television set is 20 percent of the cost. The markup is what percent of the selling price?
(markup = selling price - cost)
Options:
A)8%
B)10%
C)12 1/2%
D)15%
E)16 2/3%
Rationale: SP = 1.2CP
markup/SP = 0.2CP/1.2CP = 1/6 * 100 = 50/3 = 16 2/3%
Answer - E
Answer: E
Question: if (log5 5)(log4 9)(log3 2) is equal to
Options:
A)-1
B)2
C)3
D)4
E)1
Rationale: =>1*log 9/log 4 * log 2/log 3
=>log 3^2/log 2^2 * log 2/log 3
=>2 log 3/2log 2*log 2/log 3=1
ANSWER A
Answer: A
Question: A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares?
Options:
A)20
B)66
C)18
D)19
E)01
Rationale: Explanation:
Dividend on 1 share = (12.5 * 40)/100 = Rs.5
Rs.25 is income on an investment of Rs.100
Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20
ANSWER: A
Answer: A
Question: If a and b are nonzero integers such that 6a = 15b, then each of the following must be true EXCEPT
Options:
A)0 < b/a < 1
B)ab is positive.
C)On the number line, b lies between 0 and a.
D)The ratio of a to b is equivalent to 10/4.
E)a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that a and b are NONZERO INTEGERS and that 6a=15b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that a and b are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: E
Question: Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm?
Options:
A)188 cm2
B)150 cm2
C)168 cm2
D)198 cm2
E)225 cm2
Rationale: 1/2 * 30(9 + 6)
= 220 cm2
Answer: E
Answer: E
Question: The simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal.
Options:
A)6 1/3 % and 6 2/3 years
B)6 2/3 % and 6 1/3 years
C)6 2/3 % and 6 2/3 years
D)6 1/3 % and 6 1/3 years
E)6 % and 6 2/3 years
Rationale: Let sum = Rs. x. Then, S.l. = Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.
Rate = 6 2/3 % and
Time = 6 2/3 years = 6 years 8 months
Answer is C
Answer: C
Question: A sum of 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days.How much did C receive if all the four work together ?
Options:
A)14⁄3
B)16⁄3
C)15⁄3
D)17⁄3
E)None of these
Rationale: A's one day's work = 1⁄32
B's one day's work = 1⁄20
(B + C)'s one day's work = 1⁄12
∴ C's one day's work = 1⁄12 - 1⁄20 = 1⁄30
D's one day's work = 1⁄24
∴ (A + B + C + D)'s one day's work
1/32+1/20+1/30+1/24=75+120+80+100/2400
= 375⁄2400 = 15⁄96 = 5⁄32
∴ Out of 5⁄32 of work done
1⁄30 of the work is done by C.
⇒ Out of 25 paid for the work, C will receive
1/30 /5/32×25, i.e, 1⁄30 × 32⁄5 × 25, i.e, 16⁄3
Answer B
Answer: B
Question: If x^2+(1/x^2)=7, x^4+(1/x^4)=?
Options:
A)10
B)11
C)12
D)14
E)47
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47.
Thus, the answer is E.
Answer: E
Question: A man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
Options:
A)5.33 km
B)6.33 km
C)5.63 km
D)7.33 km
E)5.93 km
Rationale: Speed in still water = 6 kmph
Speed of the current = 2 kmph
Speed downstream = (6+2) = 8 kmph
Speed upstream = (6-2) = 4 kmph
Let the required distance be x km
Total time taken = 2 hour
x/8 +x/4 =2
x+2x/8 =2
3x/8=2
3x=16
x=5.33 km
ANSWER:A
Answer: A
Question: In a soccer bet,we play 4 teams.first team odd 1.30,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?
Options:
A)219.5
B)226.49
C)235.01
D)266.74
E)669.0
Rationale: in the case we won the bet,we have:
1.30* 5.23* 3.25* 2.0*5.00=219.50
we will win 226.49
so correct answer is B
Answer: B
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 70. He was allowed to drop his lowest score. After doing so, his average test score improved to 75. What is the lowest test score that was dropped?
Options:
A)20
B)25
C)55
D)65
E)80
Rationale: The arithmetic mean of 4 equally weighted tests was 70. So what we can assume is that we have 4 test scores, each 70.
He dropped his lowest score and the avg went to 75. This means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 70.
So the lowest score = 70 - 15 = 55
Answer (C)
Answer: C
Question: 103,100,97,..,91,88,85
Insert the missing number
Options:
A)88
B)78
C)94
D)98
E)108
Rationale: Missing number : 94
Answer : C
Answer: C
Question: In a series of consecutive numbers, 27 is the eighth smallest number and 20 is the tenth largest number. What is the range of the series?
Options:
A) 32
B) 30
C) 28
D) 16
E) 25
Rationale: Imp:All are consecutive odd numbers.
27 is the 8th smallest ,there are 7 numbers smaller then 27 ,smallest number :27-14=13
20 is the 10th largest ,so there are 9 numbers larger then 20, largest number:20+18=38
Range:38-13=25
Ans : E
Answer: E
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)88 m2
B)10 m2
C)66 m2
D)77 m2
E)31 m2
Rationale: 1/2 * 4 * 5 = 10 m2
Answer: B
Answer: B
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)Rs. 375
B)Rs. 400
C)Rs. 600
D)Rs. 800
E)Rs. 850
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 3200) =Rs.400
Answer = B
Answer: B
Question: If the height of an equilateral triangle GBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔGBC is how many times as long as a leg of the right triangle DEF?
Options:
A)(√2)/(√3)
B)(√3)/(√2)
C)√2
D)(2√2)/(√3)
E)2/(√3)
Rationale: Side of the equilateral triangle GBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle GBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Answer: D
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 7. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
Options:
A)Rs 1200
B)Rs 1500
C)Rs 1600
D)Rs 1900
E)Rs 1700
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 7x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 2100.
Hence, (R - p) = (2100 - 900) = 1200
Answer : A
Answer: A
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)19878
B)12798
C)26908
D)11750
E)22073
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Answer: D
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/2
B)1/5
C)1/3
D)1/7
E)1/9
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
C
Answer: C
Question: If books bought at prices ranging from Rs. 125 to Rs. 350 are sold at prices ranging from Rs. 170 to Rs 420, what is the greatest possible profit that might be made in selling 12 books ?
Options:
A)Rs. 3500
B)Rs. 3540
C)Rs. 3520
D)Rs. 3200
E)Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 12 books = 125*12 = Rs. 1,500
Maximum selling price of 12 books = 420 *12 = Rs. 5,040
So, maximum profit = 5040 - 1500 = Rs. 3,540
ANSWER : OPTION B
Answer: B
Question: What is the remainder when 12346 is divided by 9?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.
1+2+3+4+6 = 16
The nearest multiple of 9 is 9.
16-9= 7.
ANSWER:A
Answer: A
Question: A’s speed is 30/17 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)1/17
B)13/30
C)17/30
D)11/30
E)11/13
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 30 meters, B covers 17 meters in that time. So if the race is 30 meters long, when A reaches the finish line, B would be 13 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 13 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 30 meters) would be the same as the time required by B (to cover 17 meters) to reach the finish line.
So B should get a head start of 13/30th of the race.
Answer (B)
Answer: B
Question: Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is:
Options:
A)Rs 200
B)Rs 300
C)Rs 400
D)Rs 500
E)Rs 600
Rationale: Let C = x.
Then B = x/2
and A = x/4
A:B:C = 1:2:4.
C's share Rs.[(4/7)x700) = 400
answer :C
Answer: C
Question: In a garden, there are four blue flowers, three red flowers, four green flowers, and four pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
Options:
A)11/10
B)1/55
C)31/10
D)3/55
E)1/16
Rationale: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x3/11x2/10
= 3/55
Answer: D
Answer: D
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)9
B)7
C)8
D)6
E)4
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: C
Question: How many different positive integers are factors of 64 ?
Options:
A) 10
B) 12
C) 14
D) 16
E) 18
Rationale: 8×8=4^2 × 2^2
So total factors = (3+1)(3+1) = 16
Answer: D
Answer: D
Question: If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
Options:
A)1/16
B)3/16
C)1/8
D)3/8
E)1/2
Rationale: A) 3 heads..
all three heads can be taken as one, so total are 4- 3H,T,T,T...
3H can take any of four places= 4 ways..
B) 4 Heads..
again 3H are one but it cannot have fourth one next to it..
(i)so if we have 3H in edges.. 3H,T,_,_
the last two can be H,T or T,H--- so 2 ways..
similarily if 3H in the rightmost position-- _,_,T,3H---- 2 ways..
(ii) if we have 3H in middle... T,3H,T,H and H,T,3H,T--- 2ways..
TOTAL=2+2+2=6 ways..
C) 5 heads..
Again 3H in edges-- 3H,T,H,H or H,H,T,3H--2 ways.
we cannot have 3H in middle, as it will surely have a H adjacent to it, resulting in 4 H in a row..
D) 6 Heads--
NO possiblity..
TOTAL ways to have exactly 3H in a row=4+6+2=12 ways..
total combinations of 6 tosses= 2^6..
Probability= 12/2^6= 3/16
Answer: B.
Answer: B
Question: At a school, two-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is three-fourths the number of females, what fraction of the students speak a foreign language?
Options:
A)7/15
B)8/15
C)18/35
D)22/35
E)58/105
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (2/5)(3/7)x = (6/35)x
The number of females who speak a foreign language is (2/3)(4/7)x = (8/21)x
The total number of students who speak a foreign language is (6/35)x + (8/21)x = (58/105)x
The answer is E.
Answer: E
Question: There is a building of 100 floors
-If an egg drops from the Nth floor or above it will break.
-If it’s dropped from any floor below, it will not break.
You’re given 2 eggs.
Find N
How many drops you need to make?
Options:
A)14
B)22
C)18
D)25 sec
E)38
Rationale: A
14
This follows the below logic.
Say, the egg breaks at floor n we try to find out by going (N-1) till the first floor by doing linear search.
Say for example, I throw the egg from 10th floor, and it breaks, I wíll go to floor 1 to 9 to find out the floor..
Then I would try the same logic for every 10 floors thereby setting a worst case scenario of 19 chances.. I.e. 10,20,30,40,50,60,70,80,90,100,91,92,93,94,95,96,97,98,99
To find optimum solution, let’s try this:
If for every n, egg doesnt break, instead of going to next n, go to N-1, this would save us one drop as we are doing a linear search with second egg when egg1 breaks…
So the series would look something like this..
N + (N-1) + (N-2) + (N-3) +…+ 1
Now this is a series which is equal to N(N+1)/2
Now since it is given that the egg may or may not break from 100th floor..
We can write it as..
N(N+1)/2>=100
And n=14(approx)
So we should start from 14 then move up N-1 to 13 floor I.e. 27,39…
So the floors from where the drop needs to be done are: 14,27,39,50,60,69,77,84,90,95,99,100
So the answer is 14
Answer: A
Question: A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe
Options:
A)20.68
B)20
C)20.12
D)20.5
E)None of these
Rationale: Explanation:
Let length of other pipe be X
According to question,
30 = 45/100 X + X
30 = 0.45X + X
30 = 1.45 X
X= 30/1.45
X = 20.68m
Thus the length of the other pipe is 20.68 metres.
ANSWER A
Answer: A
Question: If 3y + 7 = x^2 + P = 7x + 5, what is the value of P ?
Options:
A)8(1/4)
B)8(1/2)
C)8(1/3)
D)8(1/5)
E)None of these
Rationale: Explanation:
3x + 7 = 7x + 5 => 7x - 3x = 2 => 4x = 2 => x = 1/2.
Now, 3x + 7 = x^2 + p => 3/2 + 7 = 1/4 + p => p = 8 * 1/4.
Answer: A
Answer: A
Question: If b is an integer, what is the greatest possible value for b that would still make the following statement true: 11*10^b < 1/10 ?
Options:
A) –4
B) –3
C) –2
D) –1
E) 0
Rationale: Just putting values, the LHS becomes
b=0 --> 11
b=-1 --> 11/10
b=-2 --> 11/100
b=-3 --> 11/1000
Anything lower will be smaller than 11/1000. b=-2, equality does not hold but it does for b=-3.
Answer is B.
Answer: B
Question: Ram singh goes to his office in the city, every day from his suburban house. His driver Mangaram drops him at the railway station in the morning and picks him up in the evening. Every evening Ram singh reaches the station at 5 o'clock. Mangaram also reaches at the same time. one day Ramsingh started early from his office and came to the station at 4 o'clock. Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early. How much time did Ram singh walk.
Options:
A)1/4 hours
B)2/4 hours
C)3/4 hours
D)5/4 hours
E)7/4 hours
Rationale: Let the time required for walk is t hours then Ram Singh will reach at the car in time (4+t), due to this walking of Ram Singh time saving = [5-(4+t)]*2 , here 2 is due to forward motion upto railway station and backward from railway station to the point where the car met to Ram Singh. It is given that time saving = 1/2 hour
so 2[1-t] = 1/2 on solving we get t = 3/4 hours
ANSWER:C
Answer: C
Question: By selling an article for 3200, a dealer suffers a loss equal to 1/5 of his investment. Find the cost price. At what price should he had sold it to make a gain of 10% ?
Options:
A)Rs. 3600, Rs. 3960
B)Rs. 4000, Rs. 4400
C)Rs. 4800, Rs. 5280
D)Rs. 4200, Rs. 5080
E)None of these
Rationale: Let his CP was X.
Loss = X/5
Selling price = CP - loss
3200 = X - (X/5)
X = 4000.
CP = Rs. 4000.
To get 10% gain,
SP = 4000 + 10% of 4000 = 4000 + 400 = Rs. 4400.
ANSWER : B
Answer: B
Question: How many words can be formed by using all the letters of the word “DAUGHTR” so that vowels always come together & vowels are never
together?
Options:
A)4320
B)760
C)720
D)4000
E)700
Rationale: Given word contains 8 different letters
When the vowels AUE are always together we may suppose
them to form an entity ,treated as one letter
then the letter to be arranged are DAHTR(AUE)
these 6 letters can be arranged in 6p6 = 6!
= 720 ways
The vowels in the group (AUE) may be arranged in 3! = 6 ways
Required number of words = 760 * 6 =4320
ANSWER A 4320
Answer: A
Question: A and B start from house at 10am. They travel on the MG road at 20kmph and 40 kmph. there is a Junction T on their path. A turns left at T junction at 12:00 noon, B reaches T earlier, and turns right. Both of them continue to travel till 2pm. What is the distance between A and B at 2 pm
Options:
A)160km
B)170km
C)180km
D)190km
E)150km
Rationale: at 12 A will travel=20*2=40km
B will travel this 40 km in 40/40=1 hr i.e. by 11am.
after T junction for A- distance travelled =2*20=40 km
for b distance travelled =40*3=120
so distance between A & B is=120+40=160km
ANSWER:A
Answer: A
Question: The average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of three of the numbers, what is the new average?
Options:
A)3.8
B)8.9
C)4.5
D)7.5
E)2.9
Rationale: Sum of 5 numbers = 5*5 =25
If 2 is subtracted from each of three of the numbers , we subtract 2*3=6 from the total sum
Sum of 5 number after subtracting 2 from each of three of the numbers =25-6=19
New average = 19/5=3.8
Answer A
Answer: A
Question: Light glows for every 30 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
Options:
A)380 times
B)142 times
C)382 times
D)392 times
E)165 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/30)=165 times.
ANSWER:E
Answer: E
Question: A military commander has to choose 3 soldiers out of a company of 5 for guarding the headquarters. How many different group combinations of 3 does he have to choose from?
Options:
A)4
B)15
C)16
D)21
E)10
Rationale: A military commander has to choose 3 soldiers out of a company of 5.
different group combinations of 3
He can do this in 5C3 ways
5*4*3/3*2*1= 10 ways
ANSWER:E
Answer: E
Question: The Average of 100, 200, 300, 400, ... , 1000 is 550. If each number is divided by 5, then the new average will be equal to
Options:
A)450
B)45
C)55
D)None of these
E)Cannot be determined
Rationale: Answer
Actual average
=( 100 + 220 + 300 + ... + 1000 ) / 10
=550
New Average = 550 / 5
=110
Correct Option: D
Answer: D
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM?
Options:
A)8 kmph
B)10 kmph
C)12 kmph
D)16 kmph
E)18 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: C