divelab/Sys2Bench huggingface dataset:
Question: A car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Let T be the total time of the trip.
30*5 + 42(T-5) = 38T
4T = 210-150
T = 15
The answer is C.
Answer: C
Question: In how many different ways could couples be picked from 8 men and 5 women?
Options:
A)8
B)5
C)13
D)40
E)20
Rationale: Number of mens = 8
Number of womens = 5
Different ways could couples be picked = 8c1 * 5c1 = 8 * 5 = 40 ways
ANSWER:D
Answer: D
Question: There are 10 copies each of 4 different books. In how many ways can they be arranged on a shelf?
Options:
A)40!
B)40!/10!
C)40!/4!
D)40!/10
E)40!/{10!^4}
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
Here we have a total of 40 books, among which 10 books of one type are identical, 10 books of another type are identical, 10 books of another type are identical, and the remaining 10 books are also identical.
Hence the number of arrangements shall be 40!/{10!10!10!10!}=40!/{10!^4}
Ans E
Answer: E
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 65.12 = ?
Options:
A)230
B)225
C)235
D)233
E)240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 65.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 65.12
= 256.3 + 40.3 – 65.12 ≈ 233
Answer D
Answer: D
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 63 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
Options:
A)14
B)45
C)54
D)65
E)81
Rationale: Just check the answers and reverse the numbers until you get 63.
81 - 18 = 63
Answer E
Answer: E
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
Options:
A)587 × 10^8 miles
B)587 × 10^10 miles
C)587 × 10^-10 miles
D)587× 10^12 ml
E)587 × 10^-12 miles
Rationale: Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 10^12 miles.
Answer: (D)
Answer: D
Question: 16 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
Options:
A)10
B)6
C)4
D)7
E)5
Rationale: Required number of machines = 16*10/40 = 4
Answer is C
Answer: C
Question: Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?
Options:
A)Rs.110
B)Rs.145
C)Rs.150
D)Rs.176
E)Rs.181
Rationale: Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B
Answer: B
Question: John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
Options:
A)6
B)9
C)36
D)120
E)720
Rationale: First place the maths book -
since all are different books, they can be arranged in 3! ways - 6 ways...
next we have 4 places for physics book, but leftmost is not a valid place as left is always maths..
_M_M_M_, but valid ways are M_M_M_
so 3 places for 3 books - again 3! ways...
Total = 3!∗3!=36
ANSWER:C
Answer: C
Question: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction W of the area of triangle ABC is the area of triangle XYZ?
Options:
A) 1/9
B) 1/8
C) 1/6
D) 1/5
E) 1/3
Rationale: If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore
Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4
dividing area of XYZ with that of ABC gives W=1/9.A
Answer: A
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price E per glass on the second day?
Options:
A) $015
B) $0.20
C) $0.30
D) $0.40
E) $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.
Answer: D.
Answer: D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)29
B)19
C)17
D)80
E)14
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face?
Options:
A)1/211
B)2/213
C)1/216
D)2/113
E)2/115
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: Which of the following values of A satisfies the inequality?
A(A – 2) = 5A – 10
Options:
A)2 < A = 5
B)2 < A = 8
C)2 < A = 6
D)2 < A = 1
E)2 < A = 2
Rationale: Explanation:
A ( A – 2) = 5 A – 10
A( A – 2) = 5 ( A – 2)
A = 5 if A – 2 > 0
A = 5, A > 2
i.e. 2 < A = 5
ANSWER: A
Answer: A
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.60 at the candy store. What is John’s weekly allowance?
Options:
A)$2.25
B)$3.00
C)$3.25
D)$3.65
E)$4.80
Rationale: x = 3x/5 + 1/3*2x/5 + 60
4x/15 = 60
x = 225 = $2.25
The answer is A.
Answer: A
Question: Out of the three numbers A, B and C, A exceeds B by 20 and C exceeds A by 55. If the sum of all the numbers is 230, What is the difference between the largest and the smallest number?
Options:
A)52
B)58
C)63
D)75
E)76
Rationale: Explanation:
We have , A = B + 20 & C = A + 55 = B + 75
Thus, (B + 20) + (B) + (B + 75) = 230
B = 45
Thus, A = 65 & C = 120. Hence, (C) – (B) = 120 – 45 = 75
Short-Cut Method : Since C is larger than A by 55 and A is larger than B by 20, we get, the Required difference = 55 + 20 = 75 (without calculating the actual values of A, B and C).
ANSWER D
Answer: D
Question: The altitude of an equilateral triangle of side 2âˆš3 cm is?
Options:
A)3/2 cm
B)1/2 cm
C)3/4 cm
D)3 cm
E)5 cm
Rationale: Explanation:
âˆš3/2*2âˆš3=3cm
ANSWER IS D
Answer: D
Question: If (x-15)(x-3) < 0, which of the following must be true?
Options:
A)x^2 + 5x + 6 < 0
B)x^2 + 5x + 6 > 0
C)15 - x >0
D)x - 5 < 0
E)11 - x > 0
Rationale: (x-15)(x-3)<0 can be written as (15-x)(x-3)>0
So,to inequality hold true multiple of (15-x) and (x-3) must be positive and if I let both elements positive/negative then the range becomes 3<x<15
Answer Choice C matched which says 15-x>0 or x<15,which must be true (I started to look from E to A for making easy decision first)
Correct Answer C
Answer: C
Question: The ratio of number of boys and girls in a school is 2:5. If there are 350 students in the school, find the number of girls in the school?
Options:
A)150
B)250
C)300
D)370
E)280
Rationale: Let the number of boys and girls be 2x and 5x
Total students = 350
Number of girls in the school = 5*350/7 = 250
Answer is B
Answer: B
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
Options:
A)36
B)77
C)89
D)16
E)22
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
Answer: A
Answer: A
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12
B)111.18
C)111.11
D)111.98
E)111.15
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.Answer: A
Answer: A
Question: The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?
Options:
A)12
B)76
C)21
D)26
E)39
Rationale: Explanation:
Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.
Answer: E
Answer: E
Question: A person's salary is getting reduced by 20%. What percentage should be added to get back his
original salary?
Options:
A)25%
B)50%
C)75%
D)85%
E)95%
Rationale: Salary he get after reduced 20% = 100-20% = 80%
So,percentage should be added to get back his salary = (20/80)*100 = 25%
ANSWER:A
Answer: A
Question: Calculate the circumference of a circular field whose radius is 10 centimeters.
Options:
A)2
B)4
C)6
D)8
E)20
Rationale: Circumference C is given by
C = 2Ï€r = 2Ï€*10 = 20 Ï€ cm
correct answer E
Answer: E
Question: If 10 men do a work in 80 days, in how many days will 20 men do it?
Options:
A)18 days
B)38 days
C)40 days
D)48 days
E)50 days
Rationale: 10 * 80 = 20 * x
x = 40 days
ANSWER:C
Answer: C
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
Options:
A)74
B)94
C)184
D)364
E)375
Rationale: L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4 = 364. Answer: Option D
Answer: D
Question: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much does the clock gain or lose in 12 hours?
Options:
A)27.273 seconds
B)29.273 seconds
C)37.273 seconds
D)47.273 seconds
E)17.273 seconds
Rationale: After 60 minute rotation the minute hand will make an angle of 30 degree with hour hand.After that let the time required to make an overtake is t minute
in this time angle covered by minute hand = (360/60)t = 6t
similarly angle covered by hour hand = (30/60)t = t/2
so for overtake 6t = 30 + t/2 or t = 60/11 min = 5 min and 5/11 min = 5 min and 300/11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds
ANSWER:A
Answer: A
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Options:
A)65 seconds
B)86 seconds
C)40 seconds
D)43 seconds
E)15 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: C
Question: Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.
Options:
A)30 days
B)45 days
C)60 days
D)90 days
E)None of these
Rationale: EXPLANATION:
Hint:
Assume that Pooja completes the job in 'x' days.
So, Aarti will take '2x' days to complete the same job.
As Pooja takes 90 days less than Aarti, we get
x = 2x – 90
By solving this equation, we get x = 90 .
Thus, 2x = 2 x 90 = 180
Part of job done by Pooja in 1 day = 1/ 90
Part of job done by Aarti in 1 day = 1/180
(Part of job done together in 1 day) = (Part of job done by Pooja in 1 day) + (Part of job done by Aarti in 1 day)
= (1/90) + (1/180)
= 3/180
=1/60
(1/60)th part of whole job will be completed by Pooja and Aarti together in one day.
Therefore, the whole job will be completed in 60 days together.
ANSWER IS C
Answer: C
Question: Haris can wash all the windows of his house in 10 hours. His wife Maggie can wash all the windows in 5 hours. How many hours will it take for both of them working together to wash all the windows?
Options:
A)2
B)3 1/3
C)4 1/4
D)5
E)6
Rationale: Work hrs=AB/(A+B)= 50/15 =3 1/3
Answer is B
Answer: B
Question: What is the smallest positive integer x, such that √392x is an integer?
Options:
A)2
B)4
C)7
D)8
E)14
Rationale: For a perfect square, the powers of prime factors should be even. 392 can be broken up as 2^3 * 7^2. You just need 2 to be multiplied to this number so that the number finally becomes 2^4 * 7^2 which is a perfect square.
Therefore x = 2.
Answer: A
Answer: A
Question: If the cost price of 110 chairs is equal to the selling price of 88 chairs, the gain percent is
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: Let C.P. of each pen be Re. 1.
Then, C.P. of 88 chairs = Rs. 88; S.P. of 88 chairs = Rs. 110.
Gain % = 22/88 * 100 = 25%
Answer:A
Answer: A
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
Options:
A)1/7
B)1/2
C)1/9
D)1/1
E)1/3
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E) = 1 - 1/2
= 1/2.
Answer: B
Answer: B
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 24% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
Options:
A)25%
B)40%
C)50%
D)55%
E)75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.24N
x = 0.6N
The percentage of rooms which permit smoking is 1 - 0.6 = 40%
The answer is B.
Answer: B
Question: Sum of the squares of three numbers is 225 and the sum of their products taken two at a time is 200. Find the sum?
Options:
A)20
B)22
C)25
D)26
E)29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 225 + 2* 200
a + b + c = √625 = 25
C
Answer: C
Question: If 2/z = 2/(z + 1) + 2/(z + 16) which of these integers could be the value of z?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:
A. 2/0 = 2/1 +2/16 INCORRECT (Division by zero)
A. 2/1 = 2/2 +2/17 INCORRECT
A. 2/2 = 2/3 +2/18 INCORRECT
A. 2/3 = 2/4 +2/19 INCORRECT
A. 2/4 = 2/5 +2/20 CORRECT
The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: E
Question: What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
Options:
A)2506
B)2578
C)2589
D)2530
E)2599
Rationale: 358/179 â€¦.. 895/179
179(2 + 3 + 4 + 5) => 2506
ANSWER A
Answer: A
Question: If Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously?
Options:
A)5
B)8
C)4
D)7
E)6
Rationale: If Total Work is X.
Ram rate of working=X/10 per day.
Gohul rate of working=X/15 per day.
Rate of work=(x/10)+(x/15)=30X/5X
=6 days
Answer is option E
Answer: E
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Options:
A)33
B)64
C)38
D)37
E)29
Rationale: Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8.
Temperature on the 5th day = 8x = 64 degrees.
Answer: B
Answer: B
Question: Find the odd man out. 241, 263, 248, 271, 255, 277, 262
Options:
A)277
B)271
C)263
D)241
E)None of these
Rationale: Explanation :
Alternatively 22 is added and 15 is subtracted from the terms. Hence, 271 is wrong
241
241 + 22 = 263
263 - 15 = 248
248 + 22 = 270
270 - 15 = 255
255 + 22 = 277
277 - 15 = 262. Answer : Option B
Answer: B
Question: A rectangular grassy plot 100 m. by 70 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 90 paise per sq. metre.
Options:
A)Rs.700
B)Rs.708.50
C)Rs.732.50
D)Rs.742.50
E)None of these
Rationale: Explanation:
Area of the plot = (100 x 70) m2 = 7000 m2
Area of the plot excluding the path = [(100 - 5) * (70 - 5)] m2 = 6175 m2.
Area of the path = (7000 - 6175) m2 = 825 m2.
Cost of gravelling the path = Rs.825 * (90/100)= Rs.742.50
Answer: Option D
Answer: D
Question: A man buys an article for 13% less than its value and sells it for 13% more than its value. His gain or loss percent is:
Options:
A)no profit, no loss
B)20% profit
C)less than 25% profit
D)more than 25% profit
E)None
Rationale: Let the article be worth Rs. x.
C.P. 87% of Rs. x = Rs. 87x/100
S.P. = 113% of Rs. x = Rs. 113x/100
Gain = (113x/100 - 87x/100) = Rs. 13x/50
Gain % = 13x/50 * 100/87x * 100 = 29 77/87 % > 25%
ANSWER:D
Answer: D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)25/5
B)25/3
C)25/2
D)25/1
E)25/9
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.Answer:C
Answer: C
Question: From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly one person in the crew has previous experience in space flight. How many different crews of this type are possible?
Options:
A)432
B)94
C)864
D)1330
E)7980
Rationale: COMB(ENN) where E=experienced and N=no previous experience
12*9*8/(2!). We divide by 2! because there are 2! ways to choose the astronauts without previous experience.
=12*9*4 = 48*9
Because 48*9 ends with a 2, look for the answer that ends with a 2. Only A suffices.
Answer: A
Question: A coin is tossed two times. What is the probability that there is at the least one tail?
Options:
A)3/4
B)31/37
C)31/18
D)31/10
E)31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed two times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/4 ; P(T) = 1 - 1/4 = 3/4
Answer: A
Answer: A
Question: Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If Q is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Options:
A) 0<y<4
B) 4<y<10
C) 10<y<20
D) 20<y<30
E) y>30
Rationale: Q Smallest prime factor is greater than 29. So answer is E
Answer: E
Question: P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
Options:
A)5
B)10
C)12
D)15
E)17
Rationale: Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10
Answer is B.
Answer: B
Question: [(9/2 ÷ 1/2 × 9/2)]/[(9/2 × 1/2 ÷ 9/2)] = ?
Options:
A)71
B)61
C)51
D)81
E)41
Rationale: Explanation:
[(9/2 ÷ 1/2 × 9/2)]/[(9/2 × 1/2 ÷ 9/2)]
= [9/2 × 2/1 × 9/2]/[9/2 × 1/2 × 2/9]
= 81/2 / 1/2 = 81/2 x 2/1 = 81
Answer: Option D
Answer: D
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 78 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
Options:
A)24
B)12
C)9
D)6
E)4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:2, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 6x : 5x : 2x
We are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
6x + 5x + 2x = 78
13x = 78
x = 6
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (2)(6) = 12
pounds of apples = (6)(6) = 36
Thus we know that there are 36 -12 = 24 more pounds of apples than grapes.
Answer is A.
Answer: A
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is 1/4 empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
Options:
A)21%
B)24%
C)22%
D)20%
E)18.75%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/4)*(3/4) = 3/16 = 18.75%
Answer (E)
Answer: E
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)35
B)37
C)41
D)43
E)44
Rationale: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
B
Answer: B
Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. How old is Janice's Daughter?
Options:
A)12
B)36
C)40
D)42
E)45
Rationale: Let Jane's age be J and daughters' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15..
IMO option A is correct answer..
Answer: A
Question: The cost of 3 kg of sugar is $12. What will the cost of 8 kg of sugar be?
Options:
A)32
B)48
C)64
D)120
E)180
Rationale: 3 kg costs $12
1 kg costs $4
8 kg costs $32
The answer is A.
Answer: A
Question: A boat goes 8 km upstream in 24 minutes. The speed of stream is 4 km/hr. The speed of boat in still water is:
Options:
A)25 km/hr
B)26 km/hr
C)22 km/hr
D)24 km/hr
E)28 km/hr
Rationale: rate upstream =8/24*60=20kmph
speed of stream=4kmph
let speed of boat in still water=xkmph
speed upstream=x-4kmph
x-4=20
x=24kmph
ANSWER:D
Answer: D