divelab/Sys2Bench huggingface dataset:
Question: Car A runs at the speed of 50km/hr & reaches its destination in 8hr. Car B runs at the speed of 25 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)4 : 1
B)11 : 8
C)13 : 7
D)15 : 7
E)16 : 9
Rationale: Sol. Distance travelled by Car A = 50 × 8 = 400 km
Distance travelled by Car B = 25 × 4 =100 km
Ratio = 400/100 = 4 : 1
Answer : A
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 18%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)44%
B)48%
C)94%
D)45%
E)39%
Rationale: g% = 18 + 18 + (18*18)/100
= 39%
Answer: E
Answer: E
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
Options:
A)9
B)11
C)17
D)21
E)27
Rationale: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
Option B
Answer: B
Question: A cycle is bought for Rs.900 and sold for Rs.1350, find the gain percent?
Options:
A)27%
B)20%
C)50%
D)30%
E)24%
Rationale: 900 ---- 450
100 ---- ? => 50%
Answer: C
Answer: C
Question: which number need to add to 859622 to get a number exactly divisible by 456?
Options:
A)454365
B)412343
C)546573
D)567683
E)859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: E
Question: What is the maximum number of pieces that a circular pizza can be cut into with 5 linear cuts?
Options:
A)10
B)14
C)15
D)16
E)17
Rationale: 1 cut makes 2 pieces
a second cut can make 4 pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
a fifth cut can make 16 pieces by cutting through 5 of the pieces
D
Answer: D
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
Options:
A)$40
B)$60
C)$80
D)$90
E)$150
Rationale: Purchase price = 150
Selling price = x
150 + 0.5*x = x
0.5*x = 150
x = 300
Profit = 300 - 150 = 150
ANSWER:E
Answer: E
Question: A meeting has to be conducted with 5 managers. Find the number of ways in which the managers be selected from among 8 managers, if 2 managers will not attend the meeting together?
Options:
A)40
B)36
C)42
D)45
E)47
Rationale: we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together
so 6C5 + (6C4 * 2C1)
this is 6 + 30=36
Answer : B
Answer: B
Question: What is the are of an equilateral triangle of side 20 cm?
Options:
A)250√3
B)150√3
C)300√3
D)200√3
E)100√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 20, Area of triangle = √3/4 * 20 * 20
= 100√3 cm2;
Answer:E
Answer: E
Question: If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 + 5x + 4
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= -1 in the equation x^2 +5x+4 = 1-5+4 = 0
E is also the answer
Answer: E
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
Options:
A)9,343
B)10,982
C)11,881
D)12,988
E)13,547
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is C.
Answer: C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)112
B)50
C)77
D)14
E)12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: B
Question: A teacher has 16 students, then she gets 7 more students. Now how many students does she have?
Options:
A)A)9
B)B)15
C)C)15
D)D)23
E)E)25
Rationale: 16+7=23. Answer is D
Answer: D
Question: Ravi can do a piece of work in 50 days while Prakash can do it in 75 days. In how many days will they finish it together?
Options:
A)30 days
B)35 days
C)25 days
D)27 days
E)29 days
Rationale: 1/50 + 1/75 = 5/150
30/1 = 30 days
ANSWER:A
Answer: A
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Options:
A)10 hours
B)16 hours
C)19 hours
D)15 hours
E)20 hours
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours
=10 hours.
Answer: A
Answer: A
Question: George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is
Options:
A)28
B)H
C)27
D)29
E)271
Rationale: Answer:B
Answer: B
Question: If x = a/(a – 1) and 1/(a – 1), then:
Options:
A)x is equal to y
B)x is equal to y only if a < 1
C)x is greater than y
D)x is greater than y only if a < 1
E)y is greater than x only if a < 1
Rationale: x = a/(a – 1) = 1 + 1/(a – 1) = 1 + y.
Therefore, x > y
ANSWER:A
Answer: A
Question: In August,a cricket team that played 120 matches won 20% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
Options:
A)40
B)52
C)68
D)80
E)98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=24+x
by solving we get x=80
ANSWER:D
Answer: D
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
Options:
A)Rs. 70
B)Rs. 71
C)Rs. 72
D)Rs. 90
E)Rs. 98
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
C
Answer: C
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 63, what is the total amount?
Options:
A)166
B)105
C)178
D)177
E)245
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 63
35 --- ? => 245
Answer: E
Answer: E
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnut purchased if you paid $19?
Options:
A)24
B)25
C)35
D)36
E)37
Rationale: a is the number of dozen of doughnuts at a price of $6/dozen
1 + 6a = 19
a= 3
The total number of doughnuts purchased -->
1 + 3 * 12 = 37
ANSWER: E
Answer: E
Question: If (4.2)x = (0.42)y = 100, then (1/x) - (1/y) =
Options:
A)1
B)2
C)1/2
D)1/4
E)2
Rationale: (4.2)x = 100
=> (42)x = 102+x
=> 42 = 10(2/x+1) ---------- (i)
[42/100]y = 100 => 42y = 102+2y
=> 42 = 102/y+2-------- (ii)
From (i) and (ii), 2/x - 2/y = 1
=>1/x - 1/y = 1/2.
ANSWER:C
Answer: C
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, 34, ?
Options:
A)31
B)47
C)36
D)31
E)33
Rationale: B
47
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: B
Question: Find the no.of ways of arranging 5 men and 5 ladies at a circular table so that no two ladies sit together ?
Options:
A)4!x4!
B)5!x5!
C)4!x5!
D)10!x10!
E)25!x25!
Rationale: The no. of ways of 5 men may be arranged in 4! ways. The ladies can arranged in themselves in 5! ways. The required no. of ways of arranging them is 4!x5! . Ans:(C)
Answer: C
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)7 kmph
B)6 kmph
C)5 kmph
D)8 kmph
E)9 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2)
= 34 kmph
Speed upstream = d/t = 45/(2 1/2)
= 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer: D
Answer: D
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜WORKâ€™, using each letter exactly once?
Options:
A)700
B)24
C)32
D)48
E)28
Rationale: The word â€˜WORKâ€™ contains 4 different letters.
Therefore, Required number of words= Number of arrangement of 4 letters, taken all at a time
=4P4
= 4!
= 4*3*2*1
= 24
ANSWER:B
Answer: B
Question: If A invested 5 times of B and at the end of the year they got a profit of Rs.36,000 in their business then share. of B in the profit was (in Rs.)
Options:
A)5000
B)4000
C)3000
D)6000
E)3500
Rationale: A:B=5:1
so b=1/6 *36000
=6000
ANSWER:D
Answer: D
Question: By selling 12 toffees for a dollar, a man loses 20%. How many for a dollar should be sell to get a gain of 20%?
Options:
A)8
B)5
C)9
D)4
E)3
Rationale: A
8
Let S.P. of 12 toffees be $x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For $3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
Answer: A
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
Options:
A)5330
B)6300
C)5343
D)5345
E)5350
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300.
B
Answer: B
Question: From a Group of 8 People, Including Sachin and Rahul, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include Sachin but not Rahul
Options:
A)5/56
B)9/56
C)15/56
D)21/56
E)25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members Sachin will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Rahul = 6
Number of ways to form a 3 member team that includes Sachin and excludes Rahul = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: C
Question: A man purchased a grinder for Rs. 120 and sold it at a profit of 10%. The selling price is:
Options:
A)Rs. 736
B)Rs. 812
C)Rs. 132
D)None of these
E)Cannot be determined
Rationale: s.p.=110/100 × 120 = 132
Answer: C
Answer: C
Question: What percent of 5 letter combinations that can be made from the letters of the word VERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
A.
B.
C.
D.
E.
Options:
A)20%
B)23.8%
C)25%
D)30.2%
E)35%
Rationale: TOTAL number of 5 letter combinations = 7P5 = 7!/2! = 3*4*5*6*7
There are 2 vowels: e,o and 5 consonants: v,r,m,n,t
If ABCDE is the required combination, A has 2 options, E has 5 options, B has 5, C has 4, and D has 3
Number of required combinations = 2*5*5*4*3
Answer = 2*5*5*4*3 / 3*4*5*6*7 = 5/21 = 23.8%
ANSWER: B
Answer: B
Question: If each data point in a certain set Q is increased by a factor of 6, what happens with the set's standard deviation?
Options:
A)Doesn't Change
B)Decreases by Factor 6
C)Increases by 6
D)Increases by Factor 6
E)Can't be determined
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 6, the standard deviation will increase proportionately, giving us answer choice D.
Answer: D
Question: if m>0 and b is m percent of a, then, in terms of m, a is what percent of b?
Options:
A)a)100m
B)b)1/100m
C)c)1/m
D)d)10/m
E)e)10^4/m
Rationale: Given (m*a)/100=b
to find (a/b)*100
Rearranging first equation
a/b*100 = 100*100/m
=10^4/m
Answer E
Answer: E
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)1
B)17
C)88
D)12
E)15
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: B
Question: On flipping 3 coins together what is the outcomes for at least one head?
Options:
A){HHH, HHT, HTH, THH, TTH, THT, TTT}
B){HHH, HHT, HTH, THH, TTH, THT, HTT}
C){HHH, HHT, HTH, TTT, TTH, THT, HTT}
D){TTT, HHT, HTH, THH, TTH, THT, HTT}
E)None
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least one heads
= favorable outcomes for exactly one heads and favorable outcomes for more than one heads
= {HHH, HHT, HTH, THH, TTH, THT, HTT}
B
Answer: B
Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 40 minutes, then the slower pipe alone will be able to fill the tank in?
Options:
A)100min
B)150min
C)200min
D)250min
E)300min
Rationale: Let the slower pipe alone fill the tank in x minutes
Then, faster pipe will fill it in x/4 minutes
1/x + 4/x = 1/40
5/x = 1/40
x = 200 min
Answer is C
Answer: C
Question: The average age of 36 students in a group is 14 years. when teacher's age is included to it, the average increases by one.What is the teacher's age in years?
Options:
A)31
B)36
C)51
D)53
E)57
Rationale: age of the teacher=(37*15-36*14)
=51 years.
ANSWER:C
Answer: C
Question: A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 90 km/hour. At what speed, in km/hr, is the car traveling?
Options:
A)70
B)80
C)74
D)75
E)78
Rationale: Time to cover 1 kilometer at 80 kilometers per hour is 1/90 hours = 3,600/90 seconds = 40 seconds;
Time to cover 1 kilometer at regular speed is 40 + 5 = 45 seconds = 45/3,600 hours = 1/80 hours;
So, we get that to cover 1 kilometer 1/80 hours is needed --> regular speed 80 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: B.
Answer: B
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 140% of John's weight. Which of these 5 people weighs the least?
Options:
A)John
B)Susan
C)Sam
D)Mark
E)Lynn
Rationale: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 140% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.4*J)=0.7*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight is more than 50%of that of John.
Answer: B.
Answer: B
Question: The sum of ages of 5 girls born at the intervals of 3 years each is 40 years. What is the age of the youngest girl
Options:
A)years
B)years
C)years
D)years
E)years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40
5x = 10
x = 2.
Age of the youngest child = x = 2 years.
A)
Answer: A
Question: If x^3 < y^2 > z, which of the statements could be true?
I. x < y < z
II. x < z < y
III. y < x < z
Options:
A)I only
B)III only
C)I and II only
D)II and III only
E)I, II and III
Rationale: Given : x^3 < y^2 > z
I. x < y < z is true for x = 3, y = 6, z = 7
II. x < z < y is true for x = 3 , y = 5 , z = 4
III. y < x < z is not true
Answer: option C
Answer: C
Question: Wendy begins sanding a kitchen floor by herself and works for 6 hours. She is then joined by Bruce, and together the two of them finish sanding the floor in 2 hours. If Bruce can sand the floor by himself in 20 hours, how long would it take Wendy to sand the floor by herself?
Options:
A)9/80 hours
B)3/20 hours
C)20/3 hours
D)80/9 hours
E)10 hours
Rationale: Let Wendy finishes sanding the floor alone in W hours while B be the hours for Bruce.
Thus in 1 hour Wendy finishes 1/w of the work while Bruce finishes 1/B of the work.
If wendy works for 6 hours and is then joined by Bruce to finish the work in 2 more hours,
6/W + 2/W+2/B = 1 (1 denotes the total amount of work)
8/W + 2/B =1 and given B =20 hours.
Thus W = 80/9 hours , D is the correct answer.
Answer: D
Question: An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
Options:
A)Rs. 52500; Rs. 47500
B)Rs. 62500; Rs. 37500
C)Rs. 72500; Rs. 27500
D)Rs. 82500; Rs. 17500
E)Rs. 72500; Rs. 17500
Rationale: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,
(x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)
(9x + 1100000 - 11x)/100 = 39000/4 = 9750
x = 62500
Sum invested at 9% = Rs. 62500
Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.
ANSWER:B
Answer: B
Question: what is summation of [3^k(28Ck)] (summation range 28 to k=0) where 28Ck is the number of ways of choosing k items from 28 items??
Options:
A)4^28
B)4^27
C)4^26
D)4^25
E)4^24
Rationale: The expansion of (1+x)^n=nC0 x^0+nC1 x^1+nC2 x^2+......
putting the value of x=3 and n=28 we get
(1+3)^28=28C0 3^0+28C1 3^1+28C2 3^2+28C3 3^3.......
which is the given summation we need to find hence,
ans= 4^28
ANSWER:A
Answer: A
Question: If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even?
Options:
A)3/5
B)17/50
C)1/8
D)51/199
E)1/4
Rationale: Another method is to enumerate the hundreds and tens digits which are acceptable:
26
28
40
42
44
In each case, any of the 5 even digits (0, 2, 4, 6, 8) can take the units place.
So acceptable cases = 5*5 = 25
Total number of integers = 200
Probability = 25/200 = 1/8
ANSWER:C
Answer: C
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?
Options:
A)1470
B)4150
C)3012
D)4430
E)5507
Rationale: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150.
ANSWER B 4150
Answer: B
Question: A and B together have Sterling 1220. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
Options:
A)Sterling 460
B)Sterling 488
C)Sterling 550
D)Sterling 664
E)None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1220 x 2/5) = Sterling 488.
Answer: Option B
Answer: B
Question: A box contains nine slips that are each labeled with one number: 1, 2, 3, 5, 8, 13, 21 and 34 Two of the slips are drawn at random from the box without replacement. What is the probability that the sum of the numbers on the two slips is equal to one of the numbers left in the box?
Options:
A)7/72
B)3/14
C)7/36
D)15/36
E)21/36
Rationale: Probability = No: of desired outcomes / Total No: of outcomes.
You are picking two slips out of 8 slips. So
Total No: of outcomes = 8C2 = 28
Desired outcome : sum of the numbers on the two slips is equal to one of the numbers left in the box. How many such outcomes are there?
If you look at the numbers closely, you will see that the following pair of numbers will give you the desired outcome.
(1,2) (2,3) (3,5) (5,8) (8,13) (13,21) . There are 6 such pairs. If the two numbers which I pick is from any of these 6 pairs, then I get my desired outcome.
So No: of desired outcomes = 6
Probability = 6/28 = 3/14
Answer :B
Answer: B
Question: Shan starts from Barabanki to Fatehpur, 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shan is at least 20km/hour fasterthan the speed of Kajol. What is the min speed of Shan to overtake Ajay, before he meets Kajol?
Options:
A)62.2 km/h
B)63 km/h
C)64.5 km/h
D)66.5 km/h
E)67.5 km/h
Rationale: Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
E)
Answer: E
Question: The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 1/5. The probability that none of them will be alive for 10 more yrs, is
Options:
A)1/2
B)1
C)2/3
D)1/5
E)2
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/5
Ans.(D)
Answer: D
Question: Grayson, a chemist, has 8 litres of a solution that contains 15% hydrochloric acid(HCI), plus unlimited 5% HCI solution. For a particular experiment, however, he needs to prepare some that contains 12% HCI. How much 5% HCI solution should be added to the 15% HCI solution to get the 12% HCI solution needed for the experiment?
Options:
A)7.6 litres
B)10 litres
C)12.8 litres
D)3.4 litres
E)8.2 litres
Rationale: 0.15(8)+0.05x = 0.12(8 + x)
Solve the equation.
0.15(8) + 0.05x = 0.12(8 + x)
1.2 + 0.05x = 0.96 + 0.12x
1.2 – 0.07x = 0.96
-0.07x = -0.24
x ≈ 3.4
Answer is D.
Answer: D
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
Options:
A)15/9 days
B)15/4 days
C)18/4 days
D)11/4 days
E)35/4 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer:B
Answer: B
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
Options:
A)Rs.1939
B)Rs.1912
C)Rs.1951
D)Rs.1908
E)Rs.1213
Rationale: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25)
= Rs. 17576 C.I.
= 17576 - 15625
= Rs.1951.
Answer:C
Answer: C
Question: A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
Options:
A)10
B)11
C)12
D)15
E)17
Rationale: Explanation:
4 a 3 |
9 8 4 } ==> a + 8 = b ==> b - a = 8
13 b 7 |
Also, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b)
(9 - b) = 0
b = 9
(b = 9 and a = 1) (a + b) = 10.
Answer: Option A
Answer: A