divelab/Sys2Bench huggingface dataset:
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 20 years. What is the age of the new member ?
Options:
A)20 years
B)21 years
C)10 years
D)23 years
E)24 years
Rationale: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 20 years then: 20*6=110+x --> x=10.
Answer: C.
Answer: C
Question: If M and N are positive integers, and the remainder obtained when M is divided by N is the same as the remainder obtained when N is divided by M, which of the following is a possible value of MN?
Options:
A) 62
B) 55
C) 42
D) 35
E) 16
Rationale: I am not too sure on this. I guess it is possible only when M and N are both same. If they are both same, MN must be a perfect square.
16 is a perfect square.
Ans:E
Answer: E
Question: A is half good a work man as B and together they finish a job in 15 days. In how many days working alone B finish the job?
Options:
A)23
B)22
C)45/2
D)36
E)48
Rationale: C
45/2
WC = 1:2
2x + x = 1/15 => x = 1/45
2x = 2/45 => 45/2 days
Answer: C
Question: Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 80% on the sale of one of the shares but a loss of 80% on the sale of the other share, then on the sale of both shares Bobby had...
Options:
A)a profit of 10
B)a profit of 8
C)a loss of 800
D)a loss of 342
E)neither a profit nor a loss
Rationale: Cost of the first stock: 96/1.8=53.33, so profit from it 96-53.33=42.67
Cost of the second stock: 96/0.2=480, so loss from it 96-480=-384
Overall loss 42.67-384=-342
Answer: D.
Answer: D
Question: Denise is trying to open a safe whose combination she does not know.
IF the safe has 4000 possible combinations,and she can try 75 different
possibilities,what is the probability that she does not pick the one
correct combination.
Options:
A)1
B)159/160
C)157/160
D)4 3/160
E)0
Rationale: When trying the first time the probability Denise doesn't pick the correct combination=3999/4000
Second time, as the total number of possible combinations reduced by one, not picking the right one would be 3998/3999.
Third time 3997/3998
...
And the same 75 times.
So we get: 3999/4000∗3998/3999∗...∗3925/39263999/4000∗3998/3999∗...∗3925/3926 every denominator but the first will cancel out and every nominator but the last will cancel out as well.
We'll get 3925/4000=157/160.
Answer: C.
Answer: C
Question: A man purchased a grinder for Rs. 600 and sold it at a profit of 12%. The selling price is:
Options:
A)Rs. 672
B)Rs. 812
C)Rs. 684
D)None of these
E)Cannot be determined
Rationale: s.p.=112/100 × 600=672
Answer: A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
A)5/16
B)5/12
C)5/87
D)5/56
E)5/38
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer:B
Answer: B
Question: If a train, travelling at a speed of 90 kmph, crosses a pole in 4 sec, then the length of train is?
Options:
A)281
B)125
C)288
D)100
E)121
Rationale: D = 90 * 5/18 * 4
= 100 m
Answer: D
Answer: D
Question: X divided by Y equals 6.32 what is a possible remainder?
Options:
A)2
B)4
C)6
D)8
E)7
Rationale: With the decimal being 32/100, the simplest form is 8/25. If the divisor is a multiple of 25, the remainder must be a multiple of 8. The only number that is so is 8. Answer D.
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 723 grams per kg, what is his percent?
Options:
A)38.3%
B)25%
C)77%
D)99%
E)12%
Rationale: 723 --- 277
100 --- ? => 38.3%
Answer: A
Answer: A
Question: Find the area of a parallelogram with base 32 cm and height 15 cm.
Options:
A)200
B)384
C)345
D)480
E)242
Rationale: Area of a parallelogram = base * height = 32 * 15 = 480 cm2
Answer: Option D
Answer: D
Question: During the first two weeks of February, the total rainfall in Springdale was 20 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall in inches during the second week of February?
Options:
A)5
B)6
C)9
D)10
E)12
Rationale: Let x be the rainfall in the first week. Then 1.5x was the rainfall in the second week.
2.5x = 20
x = 8
The rainfall during the second week was 1.5 * 8 = 12 inches
The answer is E.
Answer: E
Question: A train covers a distance of 100km in 1 hour. If its speed is decreased by 10km/hr, the time taken by the car to cover the same distance will be?
Options:
A)1hr
B)1hr 6min
C)50min
D)1hr 30min
E)1hr 45min
Rationale: Speed = 100/1 = 100km/hr
New speed = 100-10 = 90 km/hr
Time taken = 100/90 = 1hr 6min
Answer is B
Answer: B
Question: If 8 men and 2 boys working together, can do seven times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Options:
A)1:5
B)2:3
C)3:8
D)5:1
E)5:2
Rationale: 8M + 2B = 7(1M + 1B)
8M + 2B = 7M + 7B
1M = 5B
The required ratio of work done by a man and a boy = 5:1
Answer:D
Answer: D
Question: An empty pool being filled with water at a constant rate takes 3 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
Options:
A)5 hr 30 min
B)5 hr 20 min
C)4 hr 48 min
D)3 hr 12 min
E)2 hr 00 min
Rationale: (3/5) of a pool/ 2 hours = 1/5 (the rate)
(1 pools/5 hours) = (2/5* pool)/ x hours
Cross multiply x = (2/5) 5
x = 2
E
Answer: E
Question: One train is traveling 72 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Options:
A)5:4
B)5:6
C)2:1
D)5:4
E)5:1
Rationale: 72 * 5/18 = 10
20:10 => 2:1
Answer: C
Answer: C
Question: 11 times a number gives 132. The number is
Options:
A)11
B)12
C)13.2
D)None
E)Cannot be determined
Rationale: Explanation:
Let the number be 'N'
11×N=132⇒N=12
Correct Option: B
Answer: B
Question: A single letter is selected at random from the word 'PROPER'. The probability that it is a vowel is..??
Options:
A)2/11
B)3/11
C)4/11
D)0
E)2/6
Rationale: total vowels = 2, total number of letters = 6
so probability = 2/6
ANSWER:E
Answer: E
Question: A present value of a machine is $12800. Its value depletiation rate is 25% per annum then find the machine value after 3 years?
Options:
A)A)$5400
B)B)$4800
C)C)$36520
D)D)$32450
E)E)$42500
Rationale: P= $12800
R = 25%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=12800*3/4 * 3/4 * 3/4
=$5400
Answer is A
Answer: A
Question: Two pipes P and Q can fill a cistern in 15 and 10 minutes respectively. Both are opened together, but at the end of 6 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)6 1/7
B)6 1/4
C)6
D)6 1/2
E)6 1/1
Rationale: 6/15+ x/10= 1
x= 6.Answer: C
Answer: C
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 31 cm?
Options:
A)276 sq.cm
B)268 sq.cm
C)618 sq.cm
D)297 sq.cm
E)620 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 31
= 620 sq.cm.
Answer:E
Answer: E
Question: If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing thesame no. by 31
Options:
A)2
B)4
C)5
D)6
E)8
Rationale: P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 31 = 19008 / 31 = 613, remainder = 5
C
Answer: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)268 sq.units
C)167 sq.units
D)197 sq.units
E)157 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10
= 140 sq.units
Answer:A
Answer: A
Question: A cube of edge 12cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
Options:
A)5.76cm
B)8.25cm
C)11.25cm
D)15.12cm
E)20.62cm
Rationale: Increase in volume = volume of the cube = 12*12*12 cm^3
Rise in water level = volume / area = 12*12*12/20*15 = 5.76cm
Answer is A
Answer: A
Question: A ship sails 4 degrees north, then 13 S. then 17 N. then 23 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
Options:
A)0
B)1
C)2
D)4
E)None of these
Rationale: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 23 = -11
And x = 4.
Answer D
Answer: D
Question: In a competitive examination in a state A, 10% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 12% candidates got selected with 100 more candidates got selected than A. What was the number of candidates appeared from each state?
Options:
A)4000
B)5000
C)5500
D)6500
E)4200
Rationale: Let the number of candidates appeared be x
then, 12% of x - 10% of x = 100
2% of x = 100
x = 100*100/2 = 5000
Answer is B
Answer: B
Question: Three runners running around a circular track can complete one revolution in 2, 4 and 5.5 respectively. When will they meet at starting point ?
Options:
A)40 h
B)44 h
C)38 h
D)20 h
E)22 h
Rationale: Time at which they meet at starting point
= LCM of 2, 4 and 5.5
= 44 h
Answer : B
Answer: B
Question: How many cases do you need if you have to pack 500 same Dolls into cases that each hold five pair of Doll ?
Options:
A)25 cases
B)35 cases
C)50 cases
D)45 cases
E)40 cases
Rationale: D
45
500 Dolls = 225 pairs of Dolls.
225 ÷ 5= 45 cases.
Answer: D
Question: A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $30, how many pounds of premium chocolates are in the box?
Options:
A)[A] 1
B)[B] 2
C)[C] 3
D)[D] 4
E)[E] 5
Rationale: This question is a bit of Special equations with a single set of unique values.
the Equation stands : 5X + 4Y = 30
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 14 / 7 = 2
Correct Option : B
Answer: B
Question: Two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Options:
A)22 sec
B)77 sec
C)76 sec
D)21.5 sec
E)66 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 150 + 280 = 430 m.
The time required = d/s = 430/20 = 21.5 sec.
Answer:D
Answer: D
Question: It takes 60 identical printing machines 2 hours to print 300 cards. How much more time would it take 50 of these machines to print the same total?
Options:
A)20 min
B)25 min
C)26 min
D)36 min
E)30 min
Rationale: 50% of 60 = 30% or 0.30
2 hr x 60 min = 120 min
120 min x 0.30 = 36 min
It will take 36 min longer to print them with only 50 printers.
Answer is D
Answer: D
Question: Mario and Nina each have a bag of marbles, each of which contains 5 blue marbles, 10 red marbles, and 5 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
Options:
A)3/4
B)1/4
C)2/4
D)1/8
E)1/16
Rationale: Mario and Nina each select one marble from their respective bags.
Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble
Probability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)
Probability that either Mario or Nina select a red marble = 1/2
Answer would be C.
Answer: C
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.420, find the number of 50 paise coins ?
Options:
A)498
B)488
C)450
D)528
E)418
Rationale: 50*3k + 20*4k + 10*5k = 42000
280k = 42000 => k = 150
50p coins = 3k = 3*150 = 450
ANSWER:C
Answer: C
Question: The average weight of the teacher and six students is 12 kg which is reduced by 5 kg if the weight of the teacher is excluded. How much does the teacher weigh ?
Options:
A)42
B)77
C)66
D)28
E)11
Rationale: lanation:
Total age of the students and teacher together = 7 × 12 = 84
New average after excluding teacher = 6 × 7 = 42
Teachers weight = 74 - 42 = 42
Answer:A
Answer: A
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)150
C)160
D)170
E)180
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: A
Question: The remainder when 1!+2!+3!...+50! divided by 7! will be
Options:
A)21
B)873
C)777
D)927
E)19
Rationale: The remainder when the terms greater than 7! are divided by 7! becomes 0 so we need to consider the terms upto 6!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5!+6! with 7!.
So remainder is obtained by dividing (1+2+6+24+120+720)= 873 with 7! ( 5040)
So remainder is 873.
Answer:B
Answer: B
Question: In how many ways letters of the word POLICIES be arranged?
Options:
A)45326
B)28763
C)20160
D)45693
E)54823
Rationale: POLICIES has 8 letters, out of which I repeated 2 times. Hence total ways = 8! / 2! = 20160ways
C
Answer: C
Question: There are 70 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
Options:
A)20
B)31
C)42
D)53
E)64
Rationale: x + (x - 14) = 70 --> x = 42.
Answer: C.
Answer: C
Question: The sector of a circle has perimeter 83 cm and central angle 225o. Find its radius?
Options:
A)21 cm
B)15 cm
C)14 cm
D)24 cm
E)28 cm
Rationale: Let radius = x cm
Perimeter of the sector = length of the arc + 2(radius)
83= (225/360 * 2 * 22/7 * x) + 2(x)
83= 55x/14 + 2x
83 = 83x/14
1162=83x
x = 14
Answer: C
Answer: C
Question: An automobile financier claims to be lending money at S.I., but he includes the interest every six months for calculating the principal. If he is charging an interest of 20%, the effective rate of interest becomes?
Options:
A)40.5%
B)20.5%
C)10%
D)30.5%
E)50.5%
Rationale: Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 20 *1) / (100 * 2) = Rs. 10
S.I. for last 6 months = (105 * 20 * 1) / (100 * 2) = Rs. 10.5
So, amount at the end of 1 year = (100 + 10+10.5) = Rs. 120.5
Effective rate = (120.5- 100) = 20.5%.
ANSWER:B
Answer: B
Question: At a certain zoo, the ratio of sea lions to giraffes is 7 to 11. If there are 81 more giraffes than sea lions at the zoo, how many sea lions are there?
Options:
A)24
B)36
C)48
D)72
E)141
Rationale: 7/11 = x / x+81
7*81 = 4x
x=141
E. 141
Answer: E
Question: If k is the greatest positive integer such that 3^k is a divisor of 18! then k =
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: 18/3=6
18/9=2
6+2 =8
k=8
Answer:E
Answer: E
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)867 Sec
B)190 Sec
C)686 Sec
D)686 Sec
E)466 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: B
Question: Solve :
42 : 56 :: 110 : ?
Options:
A)121
B)111
C)132
D)143
E)158
Rationale: 6*7=42
7*8=56
10*11=110
11*12=132
ans 42:56::110:132
ANSWER:C
Answer: C
Question: There is a 50% chance that Alice will visit China this year, while there is a 20% chance that she will visit Brazil this year. What is the probability that Alice will visit either China or Brazil this year, but NOT both?
Options:
A)50%
B)45%
C)40%
D)35%
E)30%
Rationale: P(China but not Brazil)=0.5*0.8=0.4
P(Brazil but not China)=0.2*0.5=0.1
P(China or Brazil but not both)=0.4+0.1=0.5
The answer is A.
Answer: A
Question: A certain store sells only black shoes and brown shoes. In a certain week, the store sold x black shoes and y brown shoes. If 2/5 of all shoes sold that week were black, which of the following expressions represents the value of y, in terms of x?
Options:
A)x/3
B)x/2
C)2x/3
D)3x/2
E)2x
Rationale: x/(x+y) = 2/5
5x = 2x+2y
3x = 2y
y = 3x/2
Answer D
Answer: D
Question: In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 93% of the products of M3 III are not defective. What is the percentage of defective in the stockpile?
Options:
A)3%
B)5%
C)2.5%
D)4%
E)3.6%
Rationale: Explanation :
Let there be 100 products in the stockpile. 40% and 30% were manufactured by M1 and M2 respectively. So, 30% are manufactured by M3.
Products from M1 = 40, from M2 = 30 and from M3 = 30.
Number of defective products from M1 = 0.03 x 40 = 1.2, from M2 = 0.01 x 30 = 0.3 and from M3 = 0.07 x 30 = 2.1
Therefore, total number of defective products = 3.6
Answer : E
Answer: E
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $300 per sq. metre.
Options:
A)$2587.50
B)$3587.50
C)$4187.50
D)$6187.50
E)$8587.50
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $300
Hence, total cost
=5.5×3.75×300= $6187.50
D
Answer: D
Question: 54671 - 14456 - 33490 = ?
Options:
A)2449
B)5449
C)6749
D)6725
E)6468
Rationale: D
If we calculate we will get 6725
Answer: D
Question: A sum of money is sufficient to pay X's wages for 36 days and Y's wages for 45 days. The same money is sufficient to pay the wages of both for?
Options:
A)16
B)17
C)18
D)19
E)20
Rationale: Let the total money be $x
X's 1day work = $ x/36
Y's 1day work = $ x/45
X+Y 1day work = $ x/20
Money is sufficient to pay the wages of both for 20days
Answer is E
Answer: E
Question: The cost of 6 pens is 10 more than 5 marker's cost. The 12 pens is Rs.240.
Options:
A)Rs.11
B)Rs.42
C)Rs.24
D)Rs.110
E)Rs.22
Rationale: Let the cost of each pen and marker be 'p' and 'q' respectively.
6p - 5q = 10 --- (1)
12p= 240 . P=20
6p - 5q = 10 --- (2)
120-5q =10
=>5q = 110
=> q=22
ANSWER:E
Answer: E
Question: Find a number such that it exceeds 18 by three times the number by which it is less than 86?
Options:
A)67
B)68
C)69
D)70
E)71
Rationale: x-18=3[86-x]
x=69
ANSWER:C
Answer: C
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 85. Find the third number?
Options:
A)A)37
B)B)85
C)C)48
D)D)43
E)E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 85
6x = 85 => third number is 85.
Answer: Option B
Answer: B
Question: The ratio of football players, baseball players, soccer players, and basketball players in a school is 10:7:5:4. How many athletes are in the school if 16 players are on the basketball team?
Options:
A)40
B)92
C)104
D)208
E)80
Rationale: The ratio is 10 football players: 7 baseball players: 5 soccer players: 4 basketball players.
Divide 16 by 4 to find 1 "part" of the ratio.
16/4 = 4
Multiply 4 by 5 to find the number of soccer players.
4*5 = 20
Multiply 4 by 7 to find the number of baseball players.
4*7 = 28
Multiply 4 by 10 to find the number of football players.
4*10 = 40.
Add them all up to find total athletes.
16+20+28+40 = 104
The answer is C.
Answer: C
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 5 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Options:
A)396
B)1260
C)1155
D)7920
E)15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 5 and 11..ie., 7 possible numbers
Possible combinations for X1,X2 would be 7C2 = 21
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 21 * 55 = 1155
Ans. C
Answer: C
Question: How much does a watch lose per day, if its hands coincide ever 64 minutes?
Options:
A)32x8/11 min
B)36x8/11 min
C)90 min
D)96 min
E)None
Rationale: 55 min. spaces are covered in 60 min. 60 min. spaces are covered in (60/55 x 60) min = 65x5/11 min. Loss in 64 min.(65x5/11 - 64). = 16/11 Loss in 24 hrs(16/11x1/64x24x60)min = 32x8/11.
Answer A
Answer: A
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 3.6 miles in the sixth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
Options:
A)30
B)34
C)38
D)42
E)46
Rationale: (3.6 miles / 8 minutes)*60 minutes/hour = 27 mph
Let x be the original speed.
x - 5(3) = 27
x = 42 mph
The answer is D.
Answer: D
Question: Working at constant rate, pump X pumped out half of the water in a flooded basement in 5 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
Options:
A)a. 10
B)b. 12
C)c. 14
D)d. 26
E)e. 24
Rationale: rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
26 hours
D
Answer: D
Question: In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:
Options:
A)40 sec
B)47 sec
C)33 sec
D)35 sec
E)None of these
Rationale: speed of B=s2.
A's time of course=t.
200=s2*(t+7) ---(eq 1)
200-35=s2*t ---(eq 2)
from these 2 eqs, we get t=33sec.
ANSWER:C
Answer: C
Question: Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
Options:
A)$3.95
B)$6.65
C)$9.75
D)$7.25
E)$4.85
Rationale: John spent and gave to his two friends a total of
1.25 + 1.20 + 1.20 = $3.65
Money left
8.50 - 3.65 = $4.85
correct answer E
Answer: E
Question: A father is now three times as old as his son. NINE years back, he was four times as old as his son. The age of the son (in years) is
Options:
A)12
B)15
C)18
D)20
E)27
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-9 = 4*(S-9)
3S-9 =4S-36
S=27
F=81 years
ANSWER:E
Answer: E
Question: Six children — A, B, C, D, E and F— are going to sit in six chairs in a row. The children B & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
Options:
A)240
B)720
C)1440
D)4320
E)4800
Rationale: for such questions , we can treat both as one then total person=5.
these 5 can be arranged in 5! ways.. but within these 5 , one consists of two people who can be arranged in 2 ways BF or FB.. so ans =5!*2=240
ans A
Answer: A