divelab/Sys2Bench huggingface dataset:
Question: A butler stole wine from a butt of sherry which contained
40% of spirit and he replaced,what he had stolen by wine
containing only 16% spirit. The butt was then of 24%
strength only. How much of the butt did he steal?
Options:
A)1/3 of the butt
B)2/3 of the butt
C)1/4 of the butt
D)1/8 of the butt
E)1/9 of the butt
Rationale: Wine containing 40%spirit Wine containing 16% spirit
Wine containing 24% spirit
8 16
They must be mixed in the ratio of =1:2.
Thus 1/3 of the butt of sherry was left
hence the butler drew out 2/3 of the butt.
ANSWER : B 2/3 of the butt
Answer: B
Question: John is traveling to a meeting that is 26 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
Options:
A)25 mph
B)37 mph
C)41 mph
D)52 mph
E)56 mph
Rationale: Well 52mph. D. Time*rate=distance --> 0.5*rate=26 --> rate=52
Answer: D
Question: Find the number which is nearest to 457 and is exactly divisible by 11.
Options:
A)450
B)451
C)460
D)462
E)None
Rationale: Solution
On dividing 457 by 11, remainder is 6.
Required number is either 451 or 462
Nearest to 456 is	= 462.
Answer D
Answer: D
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.931. Find the cost of each ice-cream cup?
Options:
A)25
B)76
C)29
D)12
E)20
Rationale: Explanation:
Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 931
96 + 225 + 490 + 6x = 931
6x = 120 => x = 20.
Answer:E
Answer: E
Question: Rs. 5887 is divided between Shyam and Ram, such that Shyam's share at the end of 9 years is equal to Ram's share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.
Options:
A)2088
B)2000
C)3087
D)None of these
E)Cannot be determined
Rationale: Solution:
Shyam's share * (1+0.05)9 = Ram's share * (1 + 0.05)11
Shyam's share / Ram's share = (1 + 0.05)11 / (1+ 0.05)9 = (1+ 0.05)2 = 441/400
Therefore Shyam's share = (441/841) * 5887 = 3087.
Answer C
Answer: C
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)5
B)4
C)3
D)6
E)8
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: A
Answer: A
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, B receives:
Options:
A)s. 11,000
B)s. 11,300
C)s. 11,500
D)s. 11,700
E)s. 11,900
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (35000 x 17/50) = Rs. 11,900.
E
Answer: E
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
Options:
A)152000 m^2
B)1532500 m^2
C)153000 m^2
D)153300 m^2
E)153600 m^2
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
E)
Answer: E
Question: The average number of shirts with Salman, Ambani and Dalmiya is 69, if all of them reached a shopping mall in Delhi and purchased 12 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)81
C)62
D)can't be determined
E)None of these
Rationale: Answer
Required average
= Old average + New average
= 69 + 12 = 81
Correct Option: B
Answer: B
Question: The three competitors in a race have to be randomly chosen from a group of three men and four women. How many different such trios contain at least one woman?
Options:
A)31
B)34
C)37
D)40
E)43
Rationale: The total number of ways to choose three runners 7C3 = 35
The number of trios with only males is 3C3 = 1
The number of trios which include at least one woman is 34.
The answer is B.
Answer: B
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
Options:
A)100
B)150
C)200
D)250
E)300
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1]
= 200.
ANSWER C 200
Answer: C
Question: Lindsay can paint 1/x of a certain room in 15 minutes. What fraction of the same room can Joseph paint in 15 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)A)1/4x
B)4x/(x – 4)
C)(x – 4) / 4x
D)1/ (x – 4)
E)(x – 4) / x
Rationale: Lindsey and Joseph together can paint the room in 1 hour
in 15 mins they can paint 1/4 part of the room.
Lindsay alone paints 1/x part of the room in 15 mins
Take Joseph paints 1/y parts in 15 mins
1/x + 1/y = 1/4
1/y = 1/4 - 1/x = (x-4)/4x ANs C
Answer: C
Question: If n is a positive integer, then n*(n+1)*(n+2) is
Options:
A)even only when n is even
B)even only when n is odd
C)odd whenever n is odd
D)divisible by 3 only when n is odd
E)divisible by 4 whenever n is even
Rationale: n*(n+1)*(n+2)= +ve even integer divisible by 4 ( e.g 6,7&8)
E
Answer: E
Question: If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a + b + c ?
Options:
A)18
B)2
C)-1
D)-3
E)-4
Rationale: consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X + (X+2) + (X+4)
doing this leaves us with 3X + 6
what even number can we substitute in X to yield an answer choice
A works 18 (plug in 4 for X)
Answer: A
Question: A retailer buys 40 pens at the market price of 36 pens from a wholesaler, if he sells these pens giving a discount of 1% ,what is the profit % ?
Options:
A)5
B)10
C)15
D)20
E)None of them
Rationale: let the market price of each pen be Rs 1
then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60
profit %=((3.60*100)/36) %=10%
Answer is B.
Answer: B
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Options:
A)8 1/3
B)8 1/6
C)8 1/0
D)8 1/2
E)8 1/5
Rationale: (4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: A
Question: The average salary of all the workers in a workshop is $1000. The average salary of 5 technicians is $5000 and the average salary of the rest is $500. The total number of workers in the shop is?
Options:
A)25
B)20
C)15
D)30
E)18
Rationale: Let the total number of workers be x
1000x = 5000*5 + 500(x-5)
x = 25
Answer is A
Answer: A
Question: If 18 is 15 percent of 30 percent of a certain number, what is the number?
Options:
A)9
B)36
C)40
D)81
E)400
Rationale: Let the certain number be x.
=> (15/100)*(30/100)*x = 18;
450x=18*10000;
45x = 18000;
x=18000/45
=> x=400;
Ans is (E).
Answer: E
Question: If 9^y = 3^12, what is y?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: E
Question: An old priest fell on a bottom of the well of a church.
The well is 18 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
Options:
A)16-days
B)14-days
C)11-days
D)19-days
E)10-days
Rationale: B
14-days
In 13-days, he will climb 13-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: B
Question: Find the surface area of a cuboid 8 m long, 6 m broad and 10 m high
Options:
A)376 sq.cm
B)420 sq.cm
C)516 sq.cm
D)400 sq.cm
E)None of these
Rationale: Explanation:
Surface area = [2 (8 x 6 + 6 x 10 + 8 x 10)] cm2 = (2 x 188)cm2 = 376 cm2.
Answer: A
Answer: A
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 4 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The rate of the pump + leak = 1/4
1/2 - leak's rate = 1/4
leak's rate = 1/2 - 1/4 = 1/4
The leak will empty the tank in 4 hours.
The answer is C.
Answer: C
Question: A train leaves Mumabai at 9 am at a speed of 45 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 90 kmph. When and at what distance from Mumbai do the two trains meet?
Options:
A)287
B)279
C)90
D)278
E)379
Rationale: When the second train leaves Mumbai the first train covers 45 * 1 = 45 km
So, the distance between first train and second train is 45 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 45 / (90 -45) = 1 hours
So, the two trains meet at 2 p.m. The two trains meet 1 * 90 = 90 km away from Mumbai.
Answer:C
Answer: C
Question: On the number line, the number p is twice as many units from -2 as -2 is from 3. If p is less than –2, what is the value of p ?
Options:
A)–12
B)–10
C)–6
D)10
E)14
Rationale: Distance between -2 and 3 = 5
Since number p is twice as many units from -2 as -2 is from 3
, therefore p can be -12 Since , p is less than -2 ,
the value of p = -12
Answer A
Answer: A
Question: What is the smallest integer x for which 27^x > 3^24?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: 27^x> 3^24
Converting into the same bases:
27^x> 27^8
Therefore for the equation to hold true, x> 8 or x= 9
Option C
Answer: C
Question: Walking at 50% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
Options:
A)24
B)36
C)42
D)48
E)54
Rationale: speed is inversly proprtional to time
walking at 50% of speed meand 1/2s takes 2t.
It takes 24 minutes extra to cover the distance. then
2t=t+24
t=24.
Option A is correct
Answer: A
Question: A boy is travelling from his home to school at 6km/hr and reached 7min late. Next day he travelled at 12km/hr and reached 8min early. Distance between home and school?
Options:
A)2km
B)3km
C)4km
D)5km
E)6km
Rationale: Let the distance be x
T1 = x/6 hr
T2 = x/12hr
Difference in time = 7+8 = 15 =1/4hr
x/6-x/12 = 1/4
x/12 = 1/4
x = 3 km
Answer is B
Answer: B
Question: In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?
Options:
A)8*9!
B)7*5!
C)5*5!
D)9!
E)10*8!
Rationale: 10 examination papers arranged
consider x
and req no of arranged = 8*9!
ANSWER A
Answer: A
Question: Angelina walked 200 meters from her home to the grocery at a constant speed. She then walked 300 meters to the gym at double the speed. She spent 50 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: let the speed be X...
so time taken from home to grocery= 200/x..
the speed to gym = 2x..
so time taken = 300/2x=150/x..
its given 200/x-150/x=50..
50/x=50..
x=1m/secs..
so grocery to gym=2*1=2m/s...
Answer : A
Answer: A
Question: A volunteer organization is recruiting new members. In the fall they manage to increase their number by 7%. By the spring however membership falls by 19%. What is the total change in percentage from fall to spring?
Options:
A)16.16%
B)15.55%
C)14.44%
D)13.33%
E)12.22%
Rationale: (100%+7%)*(100%-19%) = 1.07*.81 = 0.8667
1-0.8667 = 13.33% lost = -13.33%
The Answer is D
The organization has lost 13.33% of its total volunteers from fall to spring.
Answer: D
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)278
C)282
D)202
E)270
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: A
Question: The average age of 'a' boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?
Options:
A)(ab – nc)/ (a + n) years
B)(ab + nc)/ (a - n) years
C)(ab + nc)/ (a + n) years
D)(ab – nc)/ (a - n) years
E)None of these
Rationale: (ab + nc) / (a+ n)
ANSWER:C
Answer: C
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/32
C)18/19
D)18/10
E)18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: A
Answer: A
Question: A cycle is bought for Rs.900 and sold for Rs.1350, find the gain percent?
Options:
A)39%
B)20%
C)23%
D)50%
E)83%
Rationale: 900 ---- 450
100 ---- ? =>
50%
Answer:D
Answer: D
Question: a person travels from his house to office from 11:00am to 11:30 am and covers a distance of 20km. find the average speed of the person.
Options:
A)20.1km/h
B)20.5km/h
C)21.1km/h
D)10km/h
E)20.9km/h
Rationale: time=11:30-11:00=30min=1/2hour
distance=20km
speed=20*1/2=10km/h
ANSWER:D
Answer: D
Question: If books bought at prices ranging from Rs. 90 to Rs. 190 are sold at prices ranging from Rs. 120 to Rs 260, what is the greatest possible profit that might be made in selling 21 books ?
Options:
A)Rs. 2500
B)Rs. 3000
C)Rs. 3570
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 21 books = 90*21 = Rs. 1,890
Maximum selling price of 21 books = 260 *21 = Rs. 5,460
So, maximum profit = 5460 - 1890 = Rs. 3,570
ANSWER : OPTION C
Answer: C
Question: A’s speed is 20/13 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)3/17
C)1/10
D)7/20
E)3/10
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 20 meters, B covers 13 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 7 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 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 13 meters) to reach the finish line.
So B should get a head start of 7/20th of the race.
Answer (D)
Answer: D
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 12km/hr, then find the area of square field.
Options:
A)81
B)225
C)325
D)425
E)None of these
Rationale: Explanation :
D = 12*3/2 = 18 km. So side of square is 9km, so area – 81km^2
Answer – A
Answer: A
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Options:
A)52
B)45
C)67
D)89
E)90
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER A
Answer: A
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 45 possible combinations in which Michael is not selected, what is the value of n?
Options:
A)11
B)12
C)15
D)18
E)22
Rationale: The combinations of two people, in which Michael was not selected = 45
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 90 = 10*9
Thus, n = m + 1(Michael) = 11
The answer is A.
Answer: A
Question: If U is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, U, 0, 1, 3, K, 7}?
I. -1.5
II. -2
III. 0
Options:
A) I only
B) II only
C) III only
D) I and III only
E) None
Rationale: If U is a negative integer and K is a positive integer, The answer should be (E) as S.D cannot be negative. It is only 0 if all numbers in the set are equal, which is not the case either.E
Answer: E
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)8.6%
B)6.6%
C)5.6%
D)1.6%
E)4.6%
Rationale: Explanation:
C.P. of 1 toy = 375/12 = Rs. 31.25
S.P of 1 toy = Rs. 33
Profit = 1.75/31.25 * 100 = 28/5 = 5.6%
Answer:C
Answer: C
Question: A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 65 percent of its games that season, what was the total number of games that the team played?
Options:
A)180
B)120
C)90
D)85
E)70
Rationale: 65% is 15%-points above 50% and 15%-points below 80%.
Thus the ratio of "the first 60 games" to "remaining games" is 1:1.
So the team played a total of 60+60 = 120 games.
The answer is B.
Answer: B
Question: Brand A coffee costs twice as much as brand B coffee. If a certain blend is 1/4 brand A and 3/4 brand B. what fraction of the cost of the blend is Brand A?
Options:
A)1/3
B)2/5
C)1/2
D)2/3
E)3/4
Rationale: Assume Cost of A= Ca = 200 , Cost of B = Cb=100
The blend contains 0.25 A and 0.75 B ---> Cost of the blend = Cbl = 0.25*200+0.75*100= 125
Thus fraction of A in the blend = 0.25*200/125 = 2/5. B is the correct answer.
Answer: B
Question: A rickshaw dealer buys 30 rickshaws for Rs. 4725. Of these, 8 are four-seaters and the rest are two seaters. At what price must he sell the four-seaters so that if he sells the two-two seaters at 3/4th of this price, he makes a profit 40% on his outlay?
Options:
A)Rs. 180
B)Rs. 279
C)Rs. 360
D)Rs. 450
E)None of these
Rationale: Solution: On an investment of Rs. 4725, a profit of 40% means a profit of 1890.
Hence, the targeted sales realization is Rs. 6615.
The required equation;
8p+22*(3p)/4 = 6615;
Or, 8p+(33p/2) = 6615;
In the expression for LHS = RHS; we need 33p/4 to be odd number.
This can only happen when p is not a multiple of 4.
Hence, option a and c gets eliminated automatically.
Now, we check for option b which is correct.
Answer: Option B
Answer: B
Question: The probability of two events A and B are0.25 and 0.35 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________
Options:
A)0.55
B)0.4
C)0.5
D)0.05
E)0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.35-.15
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:A
Answer: A
Question: A software engineer starts from home at 3pm for every walk on a route which has level road for some distance and a then a hillock.he walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and then down the hill at a speed of6kmph to the level ground and then at a speed of 4kmph to the home if he reaches home at 9pm.what is the distance one way of his route?
Options:
A)12km
B)15km
C)18km
D)24km
E)Data Inadequate
Rationale: time=distance/speed
so,
let the distance to the level road from home be x km
and the distance to the hillock from the level road be y km
so, (x/4+y/3)+(y/6+x/4)=6
x+y=12 km.
ANSWER:A
Answer: A
Question: In his ranch, Doug Bo can place a loop of rope, called a lasso, once in every 2 throws around a cow’s neck. What is the probability that he will be able to place a lasso around a cow’s neck at least once in 5 attempts?
Options:
A) 1/5
B) 15/32
C) 1/2
D) 31/32
E) 1
Rationale: This prompt is worded in an odd way, but essentially tells us that the probability of lasso-ing a cow is 1/2. The question asks for the probability of lasso-ing a cow AT LEAST ONCE in 5 attempts.
When it comes to probability questions, there are only 2 things that you can calculate: what you WANT to have happen OR what you DON'T WANT to have happen. Those two fractions will always add up to 1. Sometimes it's much easier to calculate what you DON'T WANT and then subtract that fraction from 1 (which will give you the probability of what you DO want).
Here, the work that would be required to calculate 1, 2, 3, 4, and 5 lasso-ings of a cow would take some time and effort. It's far easier to calculate what we DON'T WANT (0 lasso-ings) and subtract that fraction from 1.
The probability of NOT lasso-ing the cow on 5 attempts is:
(1/2)(1/2)(1/2)(1/2)(1/2) = 1/32
1 - 1/32 = 31/32
The probability of lasso-ing a cow AT LEAST ONCE in 5 attempts is 31/32
Final Answer:
D
Answer: D
Question: A and B can do a piece of work in 10 days, B and C in 5 days, C and A in 15 days. How long will C take to do it?
Options:
A)77 days
B)55 days
C)12 days
D)33 days
E)11 days
Rationale: 2c = 1/5 + 1/15 – 1/10 = 1/6
c = 1/12 => 12 days
Answer: C
Answer: C
Question: If X> 0 and X is divisible by the product of the first nine positive integers, all of the following must be factors of X except
Options:
A)35
B)40
C)63
D)315
E)704
Rationale: The question states taht X is divisible by 9!,which is 1*2*3*4*5*6*7*8*9
X=(9!) * some number
A. 35 = 5*7 so will divide X
B. 40 =5*8 so will divide X
C. 63 =9*7 so will divide X
D. 315 =5*7*9 so will divide X
E. 704 =8*8*11 This will not divide X
Ans E
Answer: E
Question: Company Z has 50 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
Options:
A)6
B)7
C)8
D)9
E)12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 50.
Now, plug options for x. Only A and E give an integer value for y. But only for E x > y as needed.
Answer: E.
Answer: E
Question: If a and b are consecutive integers (b>a), which of the following statements could be false?
1. The multiplication a+b is an even number.
2. (b/a) > 1.
3. (a + b) is always an odd number.
Options:
A)1 only.
B)2 only.
C)1 and 2 only.
D)1 and 3 only.
E)1, 2 and 3.
Rationale: Consecutive numbers means that one will be even and one will be odd.
(b/a) > 1.
If b= 1 and a=0
b/a= Undefined
Or if b =-1 and a=-2
b/a= 1/2 <1
Could be False
3. (a +b) is always an odd number.
Even+ Odd= Odd. True
C is the answer
Answer: C
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 10 million bacteria in the dish at 2: 00 p.m., at what time will there be 22.5 million bacteria in the dish?
Options:
A)6: 00 p.m.
B)8: 00 p.m.
C)6: 00 a.m.
D)8: 00 a.m.
E)10: 00 a.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 10 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time will there be 22.5 million bacteria in the dish?
Assume that there are n intervals of 2 hours between 10 million and 62.5 million.
10 * (1.5)^n = 22.5
(15/10)^n = 22.5/10 = 225/100 = (15/10)^2
Hence n = 2 intervals.
Each interval is of 2 hours. Therefore, the number of hours = 4
Adding 4 hours to 2 PM, we get 6 PM as the answer.
Option A
Answer: A
Question: A train 284 m in length crosses a telegraph post in 18 seconds. The speed of the train is?
Options:
A)77 kmph
B)55 kmph
C)57 kmph
D)58 kmph
E)76 kmph
Rationale: S = 284/18 * 18/5
= 57 kmph
Answer: C
Answer: C