divelab/Sys2Bench huggingface dataset:
Question: Donald Trump took a flight in his private jet from New York City to Los Angeles for an election rally and returned back to New York City an hour later with the same weather conditions. If the 2700 mile flight to Los Angeles took 6 hours and the flight back to New York City took 5 hrs, what was the speed of the wind in mph?
Options:
A)30 mph
B)35 mph
C)40 mph
D)45 mph
E)50 mph
Rationale: Explanation:
Change the times into minutes first.
Speed from NYC to Los Angeles: (2700/360) X 60 = 450 mph
Speed from Los Angeles to NYC: (2700/300) X 60 = 540 mph
Wind speed: 1/2 (540 - 450) = 90/2 = 45 mph
Answer: Option D
Answer: D
Question: In a division, a student took 72 as divisor instead of 36. his answer was 24 . The correct answer is-
Options:
A)42
B)32
C)48
D)28
E)38
Rationale: X/72 = 24.
X = 24 *72.
So correct answer would be,
(24 *72) /36 = 48.
ANSWER : C
Answer: C
Question: 6,11, 21, 41, 81, (...)
Options:
A)22
B)35
C)27
D)32
E)161
Rationale: Explanation :
6
6× 2 - 1 = 11
11 × 2 - 1 = 21
21 × 2 - 1 = 41
41 × 2 - 1 = 81
81 × 2 - 1 = 161
Answer : Option E
Answer: E
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity Q of the pool?
Options:
A)9000 cubic meters
B)10500 cubic meters
C)11750 cubic meters
D)12000 cubic meters
E)12500 cubic meters
Rationale: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: D
Question: If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Length is halved.
i.e., length is decreased by 50%
Breadth is tripled
i.e., breadth is increased by 200%
Formula for Change in area is:
=(-x+y-xy/100)%
=(−50+200−50×200/100)%=50%
i.e., area is increased by 50%
Answer is C.
Answer: C
Question: If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be
Options:
A)12
B)21
C)16
D)17
E)14
Rationale: 4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21
Ans: B
Answer: B
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
Options:
A)72
B)62
C)26
D)20
E)12
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
Answer:A
Answer: A
Question: The G.C.D. of 1.08, 0.33 and 0.9 is:
Options:
A)0.03
B)0.9
C)0.18
D)0.108
E)None
Rationale: EXPLANATION
Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3,
H.C.F. of given numbers = 0.03.
Answer A
Answer: A
Question: In city A, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
Is there any formula to find out directly??
Options:
A)6
B)66
C)72
D)126
E)262
Rationale: Center of the park is much important in this problem.
To pass through the park one must have to pass through this point and further to destination.
Ans = Total possible paths to destination(TPPD) - paths passing through the park (PPTP)
All possible paths covering min distance are permutation of pattern RRRRRUUUU R-> One step right / U-> One step up
Thus
TPPD = 9!/(5!x4!) = 126 (direct formula of permutation applied)
I have calculated PPTD in two steps first find all paths from origin to center of park:
1. Possible moves RRRUU total permutations 5!/(3!x2!) = 10
2. From park center to destination, in moves RRUU, total permutations as 4!/(2!x2!)=6.
Thus PPTD= 10 X 6 = 60
Ans = 126 -60 = 66
ANSWER:B
Answer: B
Question: The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?
Options:
A)25% loss
B)16 2/8% loss
C)16 3/3% loss
D)36 2/3% loss
E)56 2/3% loss
Rationale: 15 CP = 20 SP
20 --- 5 CP loss
100 --- ? => 25% loss
Answer:A
Answer: A
Question: 32.42 + 508.622 + 32.32 = ?
Options:
A)573.362
B)522.243
C)572.233
D)622.443
E)None of these
Rationale: Explanation :
32.42 + 508.622 + 32.32 = 573.362. Answer : Option A
Answer: A
Question: If 360 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
Options:
A)50
B)60
C)40
D)18
E)22
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (360 *4/24) = 60
ANSWER:B
Answer: B
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if k percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of k?
Options:
A)100p / (125 - p)
B)150p / (250 - p)
C)300p / (375 - p)
D)400k / (500 - k)
E)500p / (625 - p)
Rationale: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...
I got the answer as : 100k /(125 - .25 k)...
Multiply this equation by 4 and you get D as the answer ,...
Answer: D
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 400.01
Options:
A)88.65
B)313.65
C)300.12
D)313.56
E)315.15
Rationale: Explanation:
a - 796.21 + 498.05 = 215.50 - 400.01
a = 313.65
ANSWER: B
Answer: B
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 30min will be.
Options:
A)80 km/h
B)55 km/h
C)40 km/h
D)70 km/h
E)65 km/h
Rationale: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=30/60hr=1/2hr
New speed = 40* 2/1 kmph= 80kmph
Answer : A
Answer: A
Question: A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?
Options:
A)140 cm
B)240 cm2
C)560 cm2
D)None of these
E)Cannot be determined
Rationale: Solution
When folded along breadth, we have : 2(l/2 +b) = 34 or l + 2b = 34
When folded along length, we have : 2(l/2 +b) = 38 or 2l + b = 38
Solving (i) and (ii), we get : l = 14 and b = 10.
∴ Area of the paper = (1410) cm2 = 140 cm2 Answer A
Answer: A
Question: A man being asked how much he gave for his watch, replied; If you multiply the price by 4, and to the product add 70, and from this sum subtract 50, the remainder will be equal to 220 dollars.
Options:
A)40
B)50
C)60
D)70
E)None of these
Rationale: Solution
Let the price of the watch be represented by x
This price is to be multiplied by 4, which makes 4x
To the product, 70 is to be added, making 4x + 70
From this, 50 is to be subtracted, making 4x + 70 - 50
Here we have a number of the conditions, expressed in algebraic terms; but have as yet no equation. We must observe then, that by the last condition of the problem, the preceding terms are said to be equal to 220.
We have, therefore, this equation 4x + 70 - 50 = 220
Which reduced gives x = 50.
Here the value of x is found to be 50 dollars, which is the price of the watch.
Answer B
Answer: B
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/3 the number of cans that Karen collected and 1/4 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
Options:
A) 1/4
B) 1/3
C) 2/5
D) 1/2
E) 2/3
Rationale: John = (1/3)Karen --> Karen = 3(John)
John = 1/4(Luke) --> Luke = 4(John)
Total = 12(John)
Karen/Total = 3/12 = 1/4
Answer: A
Answer: A
Question: How many liters of pure alcohol is in a 5 liter bottle where the alcohol is at 30 percent?
Options:
A)2.5
B)2
C)1
D)3
E)1.5
Rationale: 5/10 = .5
.5 x 3 = 1.5
Answer is E
Answer: E
Question: Which of the following expressions CANNOT be equal to 0 when x^2 + 7x = -12 ?
Options:
A)x^2 + 2x − 8
B)x^2 − 4x + 3
C)x^2 − 4x − 21
D)x^2 + 2x − 3
E)x^2 +3x − 4
Rationale: x^2 +7x = -12
x^2 + 7x 12 = 0
x=-3 or x= -4
All other choices result in a possibility of 0 when you plug in -3 or -4 for x except
x^2 − 4x + 3
Answer is B
Answer: B
Question: From a Nine-member dance group, four will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer?
Options:
A)a) 1/21
B)b) 1/7
C)c) 4/21
D)d) 2/7
E)e) 1
Rationale: Total number of ways to choose 4 out of 9 = 9C4 = 2520.
Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.
P = favorable/total = 2520/2520 = 1.
Answer: E.
Answer: E
Question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8 ?
Options:
A)1
B)2
C)3
D)4
E)none of these
Rationale: A number ending in 8 can never be a perfect square.
Answer: E
Answer: E
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)228
B)236
C)120
D)988
E)266
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer:C
Answer: C
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 150 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
A)60 miles
B)80 miles
C)90 miles
D)140 miles
E)400 miles
Rationale: Answer = D. 140 miles
Relational speed = 150 - 100 = 50 miles per hour
In 3 hours, difference = 50 * 3 = 150 miles
Fast train trailing 10 miles, so effective difference = 150 - 10 = 140 miles
Answer: D
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
Options:
A)a)28
B)b)26
C)c)12
D)d)10
E)e)42
Rationale: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: C)
12=2^2+2^2+2^2
Answer: C.
Answer: C
Question: At what price must an article costing Rs.100 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)131.58
B)62.0
C)62.6
D)62.1
E)62.2
Rationale: CP = 100
SP = 100*(125/100) = 125
MP*(95/100) = 125
MP = 131.58
Answer: A
Answer: A
Question: Sheela deposits Rs. 2500 in bank savings account. If this is 25% of her monthly income. What is her monthly income in?
Options:
A)10000
B)20000
C)25000
D)22235
E)None of these
Rationale: Explanation :
25% of income = Rs. 2500
100% of income = 2500 X 100/25 = Rs. 10000
Answer : A
Answer: A
Question: The sum of three numbers is 196. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
Options:
A)60
B)30
C)38
D)48
E)None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 196
or 49x = 196 or x = 4
⇒ Second number = 15x = 15 × 4 = 60
Answer A
Answer: A
Question: A train travels from New York to Chicago, a distance of approximately 270 miles, at an average rate of 30 miles per hour and arrives in Chicago at 6:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
Options:
A)3:00
B)4:00
C)10:00
D)6:00
E)7:00
Rationale: 6:00 in evening in Chicago = 7:00 in evening in New York. So, the train was in Chicago 7:00 in the evening, New York time.
The trip took T=D/R=270/30=9 hours. Therefore, the train depart from New York at 7:00 - 9 hours = 10:00 in the morning, New York time.
Answer: C.
Answer: C
Question: Seats for Maths, Physics and Biology are in the ratio of 7 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
Options:
A)14 : 15 : 20
B)6 : 7 : 8
C)6 : 8 : 9
D)Cannot be determined
E)None of these
Rationale: Reqd ratio 7 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 7 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 14 : 15 : 20
Answer A
Answer: A
Question: A man rows his boat 120 km downstream and 92 km upstream, taking 4 hours each time. Find the speed of the stream?
Options:
A)6 kmph
B)4 kmph
C)2 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 120/(4) = 30 kmph
Speed upstream = d/t = 92/(4) = 23 kmph
The speed of the stream = (30 - 23)/2 = 4 kmph
Answer:B
Answer: B
Question: Find the odd man out
4, 15, 40, 121, 364, 1093, 3280
Options:
A)4
B)15
C)121
D)364
E)3280
Rationale: 1*3+1 = 4
4*3+1 = 13
13*3+1 = 40
40*3+1 = 121
121*3+1 = 364
364*3+1 = 1093
1093*3+1= 3280
ANSWER:B
Answer: B
Question: The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?
Options:
A)8.56 kg
B)7.76 kg
C)7.756 kg
D)6.832 kg
E)6.932 kg
Rationale: 52 * 40 * 29 = 60320
48 * 36 * 27 = 46650
------------
13664
13664 * 1/2 = 6832 => 6.832 kg
ANSWER:D
Answer: D
Question: A couple married in 1980 had two children, one in 1982 and the other in 1984. Their combined ages will equal the years of the marriage in?
Options:
A)1986
B)1985
C)1987
D)1988
E)1989
Rationale: Sum of year = 1+9+8+0 =(18) 1+8 = 9
1+9+8+2 =(20) 2+0 = 2
1+9+8+4 = (13) 1+3 = 4
Now 9+2+4= (15) 1+5= 6
Nd option A 1+9+8+6 = 24(2+4)= 6
ANSWER:A
Answer: A
Question: The length of a rectangle is five times of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 16 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 11 units?
Options:
A)180 sq.units
B)11 sq.units
C)110 sq.units
D)140 sq.units
E)220 sq.units
Rationale: Given that the area of the square = 16 sq.units
=> Side of square = âˆš16 = 4 units
The radius of the circle = side of the square =4 units
Length of the rectangle = 5* 4 = 20 units
Given that breadth = 11 units
Area of the rectangle = lb = 20 * 11 = 220 sq.units
Answer:E
Answer: E
Question: If A:B = 1/4: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:6
B)9:12:8
C)9:6:2
D)9:6:4
E)9:6:1
Rationale: A:B = 1/4:1/3 = 3:4
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:12:8
Answer:B:
Answer: B
Question: Find the odd man out
1, 2, 5, 14, 41,126
Options:
A)2
B)126
C)124
D)41
E)21
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:B
Answer: B
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $7 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 18 percent, what is the discount rate on Pony jeans?
Options:
A)9%
B)10%
C)11%
D)12%
E)15%
Rationale: You know that Fox jeans costs $15, and Pony jeans costs $18, you also know that 3 pairs of Fox jeans and 2 pairs of Pony jeans were purchased. So
3(15) = 45 - Fox
2(18) = 36 - Pony
The total discount discount is $3 and you are asked to find the percent discount of pony jeans,
so 45(18 - X)/100 + 36(X)/100 = 7 or 45*18 -45*x + 36*x =7*100 or 9x = -7*100 +45*18
x =110/9 =12.2%
E
Answer: E
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.6?
Options:
A)12.6.
B)14.4.
C)15.8.
D)16.2.
E)16.4
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer C
Answer: C
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors S does the number 4x have?
Options:
A)4y
B)3y
C)16y
D)5y
E)Cannot be determined
Rationale: I tried for x=2,4 and 6. The integral factors S for x and 4x did not have any specific relation.
My answer is E.
Answer: E
Question: A hall is 24 meters long and 12 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
Options:
A)1896
B)1912
C)2108
D)2304
E)2524
Rationale: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 2304
The answer is D.
Answer: D
Question: 5^x +25* 4^-x = 10 What is the value of x?
Options:
A)-1
B)-1/2
C)0
D)1
E)1/2
Rationale: let 5^x = t
t+ 25*1/t =10
t^2 -10t +25 =0
(t-5)^2=0
t-5=0
t=5
5^x=5
x=1
Ans: D
Answer: D
Question: There is a 5% chance that Tigers will not win at all during the whole season. There is a 5% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?
Options:
A) 55%
B) 60%
C) 70%
D) 72%
E) 95%
Rationale: There is a 5% chance that Tigers will not win at all during the whole season
We can infer that there is 95% chance Tigers will win .
Similarly There is a 5% chance that Federer will not play at all in the whole season
We can also infer that there is 95% chance that Federer will play.
Answer E
Answer: E
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)27
B)29
C)31
D)34
E)35
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
A
Answer: A
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5100. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
Options:
A)s.750, Rs.2250
B)s.2000, Rs.750
C)s.750, Rs.2000
D)s.850, Rs.2550
E)s.950, Rs.1250
Rationale: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minuâ€™s share = Rs.5100* 2/12 = Rs.850
Anuâ€™s share = Rs.5100* 6 /12 = Rs.2550
ANSWER:D
Answer: D
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is 5x-2y?
Options:
A)19
B)16
C)17
D)18
E)29
Rationale: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , 5x-2y =5* 3-2*-2 = 15+4 =19
ANSWER:A
Answer: A
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 29,000 is made?
Options:
A)Rs. 1,10,000
B)Rs. 1,20,000
C)Rs. 1,25,000
D)Rs. 1,21,000
E)None of these
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,25,000
ANSWER:C
Answer: C
Question: A train 90 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
Options:
A)11 s
B)10 s
C)6 s
D)12 s
E)None of these
Rationale: We know from the formula Time = Distance/ Speed
Thus, Time = 90/ 54 x 5/18
or, Time = 6 sec.
ANSWER:C
Answer: C
Question: Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
Options:
A)2/33
B)4/33
C)2/165
D)4/165
E)7/165
Rationale: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 5C3=10.
P(only girls are chosen)=10/165=2/33
The answer is A.
Answer: A
Question: A Cistern is filled by pipe A in 6 hrs and the full Cistern can be leaked out by an exhaust pipe B in 10 hrs. If both the pipes are opened in what time the Cistern is full?
Options:
A)15 hrs
B)16 hrs
C)17 hrs
D)14 hrs
E)18 hrs
Rationale: Pipe A can fill 1/6 of the cistern in 1 hour.
Pipe B can empty 1/10 of the cistern in 1 hour
Both Pipe A and B together can effectively fill
1/6−1/10=2/30=1/15 of the cistern in 1 hour
i.e, the cistern will be full in 15 hrs.
ANSWER:A
Answer: A
Question: What is the sum of the following series? -64, -66, -68, ..... , -100
Options:
A)-1458
B)-1558
C)-1568
D)-1664
E)None of the above
Rationale: Step by step solution
The sequence is -64, -66, -68, ..... -100.
The given set of numbers are in an arithmetic progression.
Key Data: First term is -64. The common difference is -2. The last term is -100.
Sum of the first n terms of an AP = n/2[2a1+(n−1)d]
To compute the sum, we know the first term a1 = -64 and the common difference d = -2.
We do not know the number of terms n. Let us first compute the number of terms and then find the sum of the terms.
Step to compute number of terms of the sequence
an = a1 + (n - 1)d
-100 = -64 + (n - 1)(-2)
Therefore, n = 19.
Sum Sn = 19/2[2(−64)+(19−1)(−2)]
Sn = 19/2[−128−36]
Sn = 19 * (-82) = -1558
The correct answer is Choice B.
Answer: B
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options:
A)4.3 hrs
B)8.9 hrs
C)2.9 hrs
D)7.2 hrs
E)8.6 hrs
Rationale: Net part filled in 1 hour = (1/3 - 1/10)
= 7/30
The cistern will be filled in 30/7 hrs i.e., 4.3 hrs.
Answer:A
Answer: A
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 5. Their L.C.M. is
Options:
A)48
B)22
C)56
D)60
E)35
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 5.
So, the numbers 15 and 20.
L.C.M. of 15 and 20 = 60.
Answer: Option D
Answer: D
Question: If 2x^2 + y^2 = 2xy, then (x + y)^2 =
Options:
A)x^2
B)3x^2+2y^2
C)4xy
D)2y^2
E)– y^2
Rationale: (x+y)^2 = x^2 + y^2 + 2xy = x^2 + y^2+ 2x^2+y^2 = 3x^2+2y^2
Correct option : B
Answer: B
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 50 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
Options:
A)36
B)2^4*3
C)24
D)49
E)47
Rationale: Working backward from the day it's covered:
day 50: fully covered
day 49: half covered
So 49 days
ANSWER:D
Answer: D
Question: The average of 50 numbers id 56. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
Options:
A)22.35
B)33.25
C)22.25
D)51.35
E)56.25
Rationale: Explanation:
Total of 50 numbers = (50×56)=2800
Total of 48 numbers =(2800-(45+55)]=2700
Required average = 2700/48=56.25
Answer:E
Answer: E
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)25
B)38
C)64
D)68
E)70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C