mathewhe/aqua_rat huggingface dataset:
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5seconds after he sees it strike the tree. How far is the man from the wood chopper?
(A) 2420 ft
(B) 2810 ft
(C) 1800 ft
(D) 1820 ft
(E) None of these
Rationale: Explanation:
Speed of the sound = 1100 ft/s
Time = 11/5 second
Distance = Speed × Time = 1100 ×11/5 = 220 × 11= 2420 ft
Answer: Option A
Answer: (A) 2420 ft
Question: Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
(A) 1/7
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/2
Rationale: Explanation:
One person can select one house out of 3= \inline {\color{Black}3C_{1}} ways =3.
Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.
Therefore, probability that all thre apply for the same house is 1/9
Answer: B) 1/9
Answer: (B) 1/9
Question: Tom planted vegetables in a rectangular garden that was 27 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
(A) 185 sq. ft.
(B) 186 sq. ft.
(C) 187 sq. ft.
(D) 188 sq. ft.
(E) 189 sq. ft.
Rationale: area of garden is 27 x 15 = 405 sq. ft.
1/3 x 405 = 135 sq. ft. for corn
1/5 x 405 = 81 sq. ft. for peas
135 + 81 = 216 sq. ft. used
405 - 216 = 189 sq. ft. left over
correct answer E
Answer: (E) 189 sq. ft.
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability E that both selected dogs are NOT littermates?
(A) 1/6
(B) 2/9
(C) 5/6
(D) 7/9
(E) 8/9
Rationale: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability E of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.
Again, we obtain 1 - (1/12 + 1/12) = 5/6.
Answer: C
Answer: (C) 5/6
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 6 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: Let x be the total time it takes for the cistern to fill.
6/12 + x/15 = 1
x/15 = 1/2
x = 7.5
After the first pipe is turned off, it takes 1.5 more minutes to fill the cistern.
The answer is B.
Answer: (B) 1.5
Question: Two friends C and D leave point C and point D simultaneously and travel towards Point D and Point C on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will D take to cover the entire journey between Point D and point C?
(A) 90
(B) 80
(C) 75
(D) 60
(E) 65
Rationale: Let x per minute be the speed of C and y per minute be the speed of D.
After meeting at a point, C travels for 32 mins and D travels for 50 mins. So distance covered by each of them post point of crossing
C= 32x and D=50y
The distance covered by C and D before they cross each would be distance covered by D and C post crossing respectively.
Therefore distance covered by D before he meets C= 32x
Time taken by D cover 32x distance= 32x/y mins
Therefore total time taken by D= 32x/y + 50 mins ................. I
We need to find value of x in terms of y to arrive at final answer.
Total distance= 32x+50y
Combined speed of C and D= x+y
Therefore time taken before C and D meet en-route= (32x+50y)/(x+y)
Time taken by D reach destination after meeting C= 50 mins
Total travel time for D= [(32x+50y)/(x+y)]+50 mins ...................II
Equate I and II
32x/y+50= [(32x+50y)/(x+y)]+50
(32x+50y)/y=(82x+100y)/(x+y)
32x^2+50xy+32xy+50y^2=82xy+100y^2
32x^2+82xy-82xy+50y^2-100y^2=0
32x^2-50y^2=0
32x^2=50y^2
16x^2=25y^2
Taking square root.. (since x and y denote speed, square root can't be negative)
4x=5y
y=4x/5 ............ III
substitute in I
=32x/(4x/5) + 50
=32x*5/4x + 50
=40+50
=90 mins
A
Answer: (A) 90
Question: 1/2+[(2/3*3/8)+4]-8/16=
(A) 29/16
(B) 19/16
(C) 15/16
(D) 17/4
(E) 0
Rationale: 1/2+[(2/3*3/8)+4]-8/16=
1/2+[(1/4)+4]-8/16=
1/2+[17/4]-9/16=
8/16 + 68/16 - 8/16 = 68/16=17/4
D
Answer: (D) 17/4
Question: if there is one larger cube with volume 1000 and no. of smaller cubes with volume 8.then how many small cubes are required to make a larger cube with volume of 600?
(A) 5
(B) 10
(C) 125
(D) 100
(E) 4
Rationale: the ratio between larger and smaller is
a13:a23=1000:8
a1:a2=10:2
then length of cube is 10 and 2
so make a cube with length 10, we have to 5 small cubes each in length, breadth and height. so total 125 cubes are required.
then the answer is C
Answer: (C) 125
Question: Two stations P and Q are 155 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10 am
(B) 12 am
(C) 10.30 am
(D) 12.30 am
(E) 11 am
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 155
=> 20x + 25(x-1) = 155
=> 45x = 180
=> x= 4
Means, they meet after 3 hours after 7 am, ie, they meet at 11 am
Answer is E.
Answer: (E) 11 am
Question: Anil purchased 30 kg of wheat at the rate of Rs. 22 per kg and 20 kg of wheat at the rate of Rs. 24 per kg. He mixed the two. Approximately at what rate per kg should he sell the mixture to make 25% profit?
(A) Rs. 28
(B) Rs. 29
(C) Rs. 26
(D) Rs. 282
(E) Rs. 21
Rationale: Explanation:
Total quantity of mixture = 30 + 20 = 50 kg.
By earning a profit of 25% on the total cost, the selling price of the mixture is
125/100 * (660 + 480 = 1140) = Rs. 1425
Selling price per kg = Total selling price / Total of mixture
= 1425 / 50
= Rs. 28.5
ANSWER: A
Answer: (A) Rs. 28
Question: A football player scores 2 goals in his fifth match thus increasing his average goals score by 0.1. The total number of goals in his 5 matches would be
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer C = 8 goals
If....
Total goals = 8 goals
5th game = 2 goals
1st 4 games = 6 goals
Avg. for 1st 4 games = 6/4 = 1.5 goal/game
Avg. for all 5 games = 8/5 = 1.6 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer C MUST be the answer.
Answer: (C) 8
Question: Raju is 10 years elder to Sita. 10 years from now Raju would be twice as old as sita was before 10 years. How old would be Sita after 12 years.
(A) 42 years
(B) 46 years
(C) 50 years
(D) 52 years
(E) 55 years
Rationale: If R and S are their present ages, then
R=S+10
and
R+10= 2*(S-10)
solving these eqns, we get
R=50 and S=40
At present, Sita is 40 years old.
After 12 years, Sita will be 52 years old.
ANSWER:D
Answer: (D) 52 years
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
(A) 4:6
(B) 4:9
(C) 4:3
(D) 4:1
(E) 4:2
Rationale: 12:9
= 4:3
Answer: C
Answer: (C) 4:3
Question: (1/31)+(1/32)+……+(1/61)+(1/62) is including in which of the following ranges?
(A) 2
(B) 1/2~ 1
(C) 1
(D) 1~2
(E) 1//2
Rationale: Number of terms in the given series = 32.
The lowest term is 1/62 , the largest being 1/31.
Thus, the sum of the given series will be more than
1/62 + 1/62.....1/64 (32 times)
---> 32*(1/62) = 32/62
less than 1/31 + 1/32...... 1/31 (32 times)
---> 32*(1/3) = 32/31 = 1 (approx)
B
Answer: (B) 1/2~ 1
Question: Two goods trains each 625 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22 sec
(B) 88 sec
(C) 60 sec
(D) 18 sec
(E) 9 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 625 + 625 = 1250 m.
Required time = 1250 * 6/125 = 60 sec.
Answer:C
Answer: (C) 60 sec
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 5
Rationale: Explanation:
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Answer: B
Answer: (B) 2
Question: A and B together can do a piece of work in 6 days and A alone can do it in 11 days. In how many days can B alone can do it?
(A) 12 days
(B) 15 days
(C) 66/5 days
(D) 21 days
(E) 22/5 days
Rationale: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/11 work in 1 day
B alone can do (1/6 -1/11) =5/66 work in 1 day
=> complete work can be done in 66/5 days by B
Answer: Option C
Answer: (C) 66/5 days
Question: A vendor bought bananas at 6 for a rupee. How many for a rupee must he sell to gain 20%?
(A) 2
(B) 4
(C) 7
(D) 5
(E) 3
Rationale: CP of 6 bananas = 1
Gain = 20%
SP of 6 bananas=1×120/100=12/10
⇒The number of bananas he should sell for Rs.1 for a gain of 20%=10/12∗6=10/2=5
ANSWER:D
Answer: (D) 5
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits H equal to 28?
(A) 14
(B) 24
(C) 28
(D) 48
(E) 96
Rationale: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So H=24+24=48.D
Answer: (D) 48
Question: If a 10% deposit amounting to $110 has been paid toward buying a brand new TV, how much remains to be paid?
(A) $880
(B) $990
(C) $1000
(D) $1100
(E) $1210
Rationale: Explanation:
Let's start with what the total price of the TV would be. If 10% is equal to $110 then 100% equals $x. We just have to multiply $110 by 10 to get total amount=$1100. Out of this amount we then need to deduct the amount already paid which was $110 so we have $1100-$110=$990
Answer: Option B
Answer: (B) $990
Question: In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(A) 30
(B) 10
(C) 18
(D) 28
(E) 32
Rationale: Total=English+German-Both+Neither --> 52=English+22-12+0 --> English=42 --> Only English=English-Both=42-12=30
Answer: A.
Answer: (A) 30
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 229
(B) 87
(C) 26
(D) 12
(E) 667
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Answer: (D) 12
Question: A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
(A) 53
(B) 54
(C) 55
(D) 56
(E) 57
Rationale: 12.4*x+26=(4+x)12
solve equation x=55
ANSWER:C
Answer: (C) 55
Question: There are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
(A) 27
(B) 32
(C) 35
(D) 30
(E) 45
Rationale: Explanation:
HCF (408, 240) = 24
The number of boys or girls that can be placed in a section = 24.
Thus the total number of sections is given by
408/24+240/24 =17+10 = 27
Answer: A
Answer: (A) 27
Question: If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss.
(A) 50
(B) 60
(C) 70
(D) 20
(E) 90
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $6
So he sold 10 lollipops for $(10 × 6) = $60
Loss = $(80 – 60) = $20
answer :D
Therefore, loss = $ 20.
Answer: (D) 20
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :
(A) 6000
(B) 7000
(C) 8888
(D) 9000
(E) None of these
Rationale: Explanation:
Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000. Answer: D
Answer: (D) 9000
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 1.99 km
(B) 2.88 km
(C) 4.49 km
(D) 2.99 km
(E) 7.88 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88 km
Question: A runs times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
(A) 200
(B) 378
(C) 277
(D) 298
(E) 797
Rationale: Explanation:
Ratio of the speeds of A and B =5 : 1 = 5 :3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of \inline \fn_jvn {\color{Black} \left ( \frac{5}{2}\times 80 \right )} m =200m
\inline \fn_jvn {\color{Black} \therefore }Winning post is 200 m away from the starting point.
Answer: A) 200 m
Answer: (A) 200
Question: 2, 4, 6, 8, 10, ... ?
(A) 8
(B) 5
(C) 7
(D) 3
(E) 12
Rationale: Each number increases by 2.
2+2=4
4+2=6
6+2=8
8+2=10
10+2=12
ANSWER:E
Answer: (E) 12
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Explanation:
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Answer: (B) 21
Question: What is the value of 10^8- 6^4?
(A) 9,99,98,623
(B) 9,99,98,704
(C) 9,99,98,800
(D) 9,99,99,521
(E) 9,99,99,932
Rationale: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer B
Answer: (B) 9,99,98,704
Question: Which of the following is a parallelogram?
(A) 130,50,130,50(angle in deg)
(B) 120,30,130,20(angle in deg)
(C) 95,95,95,95(angle in deg)
(D) a & c
(E) none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:A
Answer: (A) 130,50,130,50(angle in deg)
Question: If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case.What is the sum of the digits of N ?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 4
Rationale: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
ANSWER:E
Answer: (E) 4
Question: The cost of producing x tools by a company is given by
C(x) = 2000 x + 5500 (in $)
a) What is the cost of 100 tools?
(A) 215500 $
(B) 205800 $
(C) 125900 $
(D) 226500 $
(E) 205500 $
Rationale: Solution
C(100) = 2000*100 + 5500 = 205500 $
Answer E
Answer: (E) 205500 $
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
(A) 153
(B) 150
(C) 137
(D) 132
(E) 89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 132
=> x = 88
Verify. 88 + 44 = 132
Answer is D
Answer: (D) 132
Question: What is the next term in the below series.
1/5 , 1/2 , 1/3 , 2/5 ,1, 2/3, 3/5, 1 1/2 ,1, 4/5,?
(A) 1/5
(B) 0
(C) 2
(D) 2/5
(E) 3/5
Rationale: 1/5 2/5 3/5 4/5
1/2 1 1 1/2 ?
1/3 2/3 1 4/3
ans :2
ANSWER:C
Answer: (C) 2
Question: The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: First decrease in percent
part / whole = (120 - 100) / 120 = 0.17 = 17%
Second decrease in percent
part / whole = (100 - 80) / 100 = 0.20 = 20%
The second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease.
Answer B
Answer: (B) 20%
Question: The distance traveled by eagle in one year approximately 150,000,000 miles.The distance traveled by eagle in 50 years?
(A) 10<8>
(B) 10<16>
(C) 10<4>
(D) 10<12>
(E) 10<11>
Rationale: The distance traveled by eagle in one year = 150,000,000 miles.
The distance traveled by eagle in 50 years = 150,000,000 miles * 50 years = 7,500,000,000 miles
(ie) 75*10<8> exponent Answer : A
Answer: (A) 10<8>
Question: A committee of 5 people is to be selected from 8 people. How many different committees are possible?
(A) 28
(B) 40
(C) 56
(D) 168
(E) 336
Rationale: Because the order does not matter in selecting 5 people for the committee, this is a combination question.
The number of ways to select 5 people from 8 = 8C5 = 8!/5!*3! = 56. Hence C.
Answer: (C) 56
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: Option A
Answer: (A) 2.5
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 3m
(B) 5m
(C) 8m
(D) 2m
(E) 1m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Answer: (D) 2m
Question: Three friends James, David and Charlie divide $1230 amongs them in such a way that if $5, $10 and $15 are removed from the sums that James, David and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9: 10 : 11. How much did Charlie receive?
(A) $600
(B) $575
(C) $550
(D) $580
(E) $615
Rationale: A+B+C = 1230
Given ratio 9:10:11
Let us say the shares of A,B,C deducting 5,10,15 be a,b,c
a+b+c = 1230-30= 1200 = 30K
c share = (1200X30)/60 = 600
C = charlie share = 600+15= 615
Option E
Answer: (E) $615
Question: A water tank is three-fifths full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10
Since the rate is negative, the tank will be emptied.
A full tank would take 10 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 10 = 6 minutes
The answer is C.
Answer: (C) 6
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 30 kms. what was the total distance traveled in 12 hours?
(A) 252 kms
(B) 152 kms
(C) 492 kms
(D) 752 kms
(E) 152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(30+32+34+.....upto 12 terms)
This is an A.P with first term, a=30, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 30+{12-1) x 2]
= 6(82)
= 492 kms.
Answer: C
Answer: (C) 492 kms
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 95 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 155 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
(A) 138
(B) 148
(C) 150
(D) 162
(E) 186
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 186min
* leg A-B ---> d = 95.186/60 = 17670/60
* leg B-A ----> d = 155*114/60 = 17670/60
so the correct ans. isE
Answer: (E) 186
Question: A train ,155 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 270 m
(B) 245 m
(C) 235 m
(D) 220 m
(E) 240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 155+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (155+x)/30 m/s
=> 45 Ã— (10/36) = (155+x)/30
=> 45 Ã— 10 Ã— 30 /36 = 155+x
=> 45 Ã— 10 Ã— 10 / 12 = 155+x
=> 15 Ã— 10 Ã— 10 / 4 = 155+x
=> 15 Ã— 25 = 155+x = 375
=> x = 375-155 =220
Answer: Option D
Answer: (D) 220 m
Question: There are 7 players in a bowling team with an average weight of 112 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
(A) 115 Kg.
(B) 110 Kg.
(C) 106 Kg.
(D) 105 Kg.
(E) 100 Kg.
Rationale: The New average will be= (112*7+110+60)/9= 106 kgs
C is the answer
Answer: (C) 106 Kg.
Question: A can have a piece of work done in 5 days, B can work three times faster than the A, C can work four times faster than A. How many days will they take to do the work together ?
(A) 3 days
(B) 8/9 days
(C) 3/2 days
(D) can't say
(E) none
Rationale: A's 1 day work is 1/12
B's 1 day work is 3/12
C's 1 day work is 4/12
(A+B+C)'s 1 day work(1/12+3/12+4/12) is 2/3
so, they can finish the work in 3/2 days
ANSWER:C
Answer: (C) 3/2 days
Question: There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters ?
(A) 18!
(B) 2! x 19!
(C) 19!
(D) 17!
(E) None of these
Rationale: First arrange the two sisters around a circle in such a way that there will be one seat vacant between them. [This can be done in 2! ways since the arrangement is not circular.]
Then, the other 18 people can be arranged on 18 seats in 18! ways.So, total number of ways = 18! x 2! ways
ANSWER:E
Answer: (E) None of these
Question: In a camp,there is a meal for 120 men or 200 children.If 180 children have taken the meal,how many men will be catered to with the remaining meal ?
(A) 20
(B) 30
(C) 12
(D) 50
(E) 60
Rationale: Solution
There is a metal for 200 children. 180 children have taken the meal.
Remaining meal is to be catered to 20 children.
Now, 200 children = 120 men
20 children =( 120/200x20)men= 12 men. Answer C
Answer: (C) 12