divelab/Sys2Bench huggingface dataset:
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 865 in 4 years. The sum is:
Options:
A)s. 665
B)s. 690
C)s. 698
D)s. 700
E)s. 720
Rationale: S.I. for 1 year = Rs. (865 - 815) = Rs. 50.
S.I. for 3 years = Rs.(50 x 3) = Rs. 150.
Principal = Rs. (815 - 150) = Rs. 665.
Answer: Option A
Answer: A
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 20%. What was its profit on the items sold in February?
Options:
A)20%
B)30%
C)35%
D)37.5%
E)40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.8*150x = 120x
Hence total profit = 20%
Option A
Answer: A
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 16 hrs and a machine of type S does the same job in 8 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Options:
A)A)3
B)B)4
C)C)6
D)D)9
E)E)12
Rationale: Rate of machine R =1/16
Rate of machine S =1/8
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/16 +x/8 =1/2
3x/16=1/2
x=16/6=3
So no of machine R is 3
Answer A
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Options:
A)12/458
B)12/455
C)12/455
D)12/451
E)12/452
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.Answer: C
Answer: C
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)40%
B)47%
C)50%
D)59%
E)60%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
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)1/8
B)1/2
C)1/6
D)1/5
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: Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 3/4 brand X and 1/4 brand Y. what fraction of the cost of the blend is Brand X?
Options:
A)a. 6/7
B)b. 2/5
C)3. 1/2
D)4. 2/3
E)5. 3/4
Rationale: Assume Cost of X= Ca = 200 , Cost of Y = Cb=100
The blend contains 0.75 X and 0.25 Y ---> Cost of the blend = Cbl = 0.75*200+0.25*100= 175
Thus fraction of X in the blend = 0.75*200/175 = 6/7.
Answer : A
Answer: A
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 75 km more than the other. What is the distance between the two stations?
Options:
A)540 km
B)675 km
C)276 km
D)178 km
E)176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 75km more than the other,
25x â€“ 20x = 75
5x = 75
x = 15 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*15 = 675 km.
ANSWER: B
Answer: B
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 25 percent of the total votes?
Options:
A)6.25%
B)12.5%
C)15%
D)17.5%
E)20%
Rationale: There were 80% of the votes remaining and he needed 5%/80% = 1/16 = 6.25%
The answer is A.
Answer: A
Question: The speed of a car is 120 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)89 kmph
B)92 kmph
C)90 kmph
D)65 kmph
E)77 kmph
Rationale: S = (120 + 60)/2 = 90 kmph
C
Answer: C
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Time from 7 am to 4.15 pm = 9 hrs 15 min = hrs
3 min. 5 sec. of this clock = 3 min. of the correct clock.
hrs of this clock = hrs of the correct clock
hrs of clock = hrs of the correct clock.
=9 hrs of the correct clock.
The correct time is 9 hrs after 7 am. i.e., 4 pm.
Answer: A) 4pm
Answer: A
Question: Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $128 and $140 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
Options:
A)640
B)720
C)1080
D)1200
E)1440
Rationale: $128 for 2 years = $64 per year.
Extra $12 yearned with the compound interest is the percent yearned on percent. So, $12 is yearned on $64, which means that the interest = 5%.
This on the other hand means that half of the savings = 64*5 = $320. Twice of that = $640.
Answer: A.
Answer: A
Question: Find the average of all the numbers between 6 and 34 which are divisible by 6.
Options:
A)18
B)20
C)24
D)30
E)21
Rationale: Solution
Average	= ((12+18+24+30)/5)
= 84 / 4
= 21.
Answer E
Answer: E
Question: There are 6 more women than there are men on a local co-ed softball team. If there are a total of 24 players on the team, what is the ratio of men to women?
Options:
A)10/16
B)9/15
C)4/16
D)6/10
E)4/10
Rationale: w = m+6
w+m = 24
m+6+m = 24
2m = 18
m = 9
w = 15
ratio:9:15
Ans: B
Answer: B
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
Options:
A)4 : 9
B)4 : 3
C)4 : 12
D)4 : 8
E)4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.
Answer: B
Answer: B
Question: The profits of QRS company rose 40% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
Options:
A)15%
B)32%
C)40%
D)68%
E)80%
Rationale: Assume 100 in march , then 140 in April as 40% increase , Then 112 in may as 20% decrease from April , and then 168 in june which is 150% of 112 .
So overall increase is from 100 to 168 is 68%
Answer D
Answer: D
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
Options:
A)8/15
B)7/15
C)11/15
D)2/11
E)7/11
Rationale: Explanation :
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
Answer : Option A
Answer: A
Question: The length of a room is 6.5 m and width is 2.75 m. What is the cost of paying the floor by slabs at the rate of Rs.600 per sq. metre.
Options:
A)Rs.18725
B)Rs.16725
C)Rs.30725
D)Rs.10725
E)Rs.20725
Rationale: Area =6.5*2.75 sq. metre.
Cost for sq. metre. = Rs.600
Hence, total cost=6.5*2.75*600
=Rs.10725
ANSWER:D
Answer: D
Question: . In digging a pond 22 m * 12 m * 5 m the volumes of the soil extracted will be?
Options:
A)3223
B)1320
C)1400
D)1560
E)3000
Rationale: 22 * 12 * 5 = 1320
Answer: B
Answer: B
Question: A sum fetched a total simple interest of $4106.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options:
A)$8829
B)$2840
C)$6578
D)$7782
E)$8927
Rationale: E
8927
Principal
= $100 x 4106.25/9 x 5
= $410625/45
= $8927.
Answer: E
Question: In a group of 25 factory workers, 14 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 14
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 6 are men. (B - 8= 14- 8= 6)
So 6 out of 11 men have brown eyes.
E
Answer: E
Question: A circular mat with diameter 3.5 inches is placed on a square tabletop, each of whose sides is 6 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (22/7)(3.5)(3.5)
Area of the Table = (6)(6)
So the quick way to estimate is looking at the fraction like this:38.5/36 nearest to 1
Answer: B
Answer: B
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 6.5 km apart, if they walk in the same direction?
Options:
A)12 hrs
B)13 hrs
C)15 hrs
D)17 hrs
E)None
Rationale: Sol.
to be 0.5 km apart, they take 1 hour.
To be 6.5 km apart, they take [1/0.5 * 6.5] hrs = 13 hrs.
Answer B
Answer: B
Question: If the cost price of 18 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
Options:
A)20% loss
B)12.5% profit
C)33.33 % loss
D)30.33% loss
E)None of these
Rationale: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 18 articles = Rs. 18.
Selling price of 16 articles = Rs. 18
Therefore, Selling price of 18 articles is :-
=>18/16Ã—18
=>20.25.
Therefore, Profit = Selling price - Cost price.
=>20.25âˆ’18=2.25.
Hence, the percentage of profit = profit x 100/C.P.
=>2.25/18Ã—100.
=>12.5% Profit.
Answer : B
Answer: B
Question: In a 400 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
Options:
A)85
B)83
C)82
D)84
E)86
Rationale: Solution simple
Out of 400 20% are male i.e 80 and 25% are female i.e 100 , so total homeowner is 180.
Now min number homeowner is 80 and max is 180 so question ask us to find least and 82 has least value among all option.
So ans is 82.
Ans: C
Answer: C
Question: On 6th July, 2017 Thursday falls. What day of the week was it on 6th July, 2016?
Options:
A)Saturday
B)Sunday
C)Monday
D)Tuesday
E)Wednesday
Rationale: Explanation:
6th July 2017 – 6th July 2016 = 52 weeks 1 day. So July 6th 2016 is behind one day = Wednesday
Answer: E
Answer: E
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 800 pounds of the seed mixture?
Options:
A)6
B)12
C)20
D)24
E)120
Rationale: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
800 / 40 = 20 acres
The answer is C.
Answer: C
Question: An error 6% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Options:
A)12.04%
B)14.14%
C)12.36%
D)12.26%
E)15.5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (106 x 106) cm2.
(A2 - A1) = [(106)2 - (100)2]
= (106 + 100) x (106 - 100)
= 1236 cm2.
Percentage error = 12.36%
D
Answer: D
Question: At 15:15 pm railway time, what will be the angle between minute and hour hand?
Options:
A)238
B)360
C)377
D)277
E)291
Rationale: At 15:15 both minute and hour hands will be in same position. Hence the angle between them will be zero
degrees. However 360 degree also means both minute and hour hands are in same position. Hence correct answers are
both zero and 360 degrees
Answer:B
Answer: B
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 5% and the mobile phone at a profit of 10%. Overall how much he make a profit.
Options:
A)s. 90
B)s. 120
C)s. 200
D)s. 50
E)s. 290
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 5/100) = 15000 - 750
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50
As this is positive, an overall profit of Rs. 50 was made.
D
Answer: D
Question: Out of first 45 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
Options:
A)17/45
B)7/45
C)17/9
D)7/9
E)17/27
Rationale: n(S) = 45
n(Even no) = 22= n(E)
n(Prime no) = 14 = n(P)
P(EᴜP)
= 22/45 + 14/45 - 1/45
= 35/45=7/9
Answer:D
Answer: D
Question: Two of his favorite buildings are Chicago’s Sears (Willis) Tower and
Dubai’s Burj Khalifa. If Burj Khalifa stands at 830 meters high and
Sears stands at 527 meters high, how much higher is Burj Khalifa than Sears?
Options:
A)300
B)250
C)130
D)303
E)111
Rationale: 830-527=303. Answer is D.
Answer: D
Question: present ages of Ram and Rahim are in the ratio of 4:3 respectively. Four years ago, the ratio of their ages was 16:11 respectively . what Ram's present age in years?
Options:
A)27
B)24
C)40
D)20
E)35
Rationale: Ram and Rahim be 4x years and 3x years respectively
(4x-4)/(3x-4)=16/11
11(4x-4)= 16(3x-4), 44x-44=48x-64
x=5, therefore Ram's present age : 4x= 20 years
correct answer(D)
Answer: D
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5 feet 6 nches. Find the % correction made by the candidate from his stated height to his actual height?
Options:
A)15
B)20
C)18
D)16.5
E)25
Rationale: His height was = 5 feet 6 inch = 6 + 60 = 66 inch. Required % correction =66*(1.25-1) = 16.5
D
Answer: D
Question: There are 6 people and 3chairs. In how many ways people can occupy the chairs?
Options:
A)120
B)150
C)240
D)60
E)100
Rationale: total people = 6
total chairs = 3
1st chair can be occupy in 6ways
2nd chair can be occupy in 5ways
3rd chair can be occupy in 4ways
total number of ways = 6*5*4 = 120 ways
correct option is A
Answer: A
Question: A man's speed with the current is 16 km/hr and the speed of the current is 3.2 km/hr. The man's speed against the current is
Options:
A)9
B)9.6
C)11
D)12
E)13
Rationale: Man's rate in still water = (16 - 3.2) km/hr = 12.8 km/hr.
Man's rate against the current = (12.8 - 3.2) km/hr = 9.6 km/hr.
Answer:B
Answer: B
Question: A certain series is defined by the following recursive rule: Se=K(Se-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term?
Options:
A)ROOT 2
B)ROOT 3
C)64*ROOT 3
D)64*3^1/3
E)64*3^24
Rationale: Ans...D
No need for any GP formula here
The rule is that eth term is K times the (e-1)th term.
1st = 64
2nd = k.64
3rd = k^2.64
.
.
.
9th term = k^8 *64
.
.
.
so 25th = k^24*64
Using this solve for k and substitute k in the equation for the 9th term
Answer: D
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)Rs.250
B)Rs.280
C)Rs.290
D)Rs.300
E)Rs.380
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
A)
Answer: A
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 676 feet squared, what is the difference between the length and the width of the roof?
Options:
A)39.
B)40.
C)42.
D)44.
E)46.
Rationale: Let the width= x
x*4x=676
x^2= 169
x= 13
Length= 4*13= 52
difference= 52-13= 39
A is the answer
Answer: A
Question: In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 3:2:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
Options:
A) $600
B) $720
C) $675
D) $450
E) $225
Rationale: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:
Household Expenses : Food : Miscellaneous = 3x : 2x : x
Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:
3x + 2x + x = 1,800
6x = 1,800
x =300
Thus, the total amount allocated to food is 2 x 300 = $600.
Answer A.
Answer: A
Question: A company has 65 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made ​​the three courses. How many employees have no training?
Options:
A)A)0
B)B)9
C)C)10
D)D)11
E)E)25
Rationale: Total employees=65
studied accounting=22
studied finance=15
studied marketing=14
9 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-9-(2*1)
=51-11
=40
Employees with no training
=65-40
=25
Ans=E
Answer: E
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)44%
B)49%
C)84%
D)24%
E)45%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: A
Answer: A
Question: It takes Avery 2 hours to build a brick wall while Tom can do it in 4 hour. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
Options:
A)70
B)20
C)50
D)60
E)30
Rationale: Avery takes 2 hours
Tom takes 4 hours
Efficiency of Avery is 1/2 units/hr
Efficiency of Tom is 1/4 units/hr
Combined efficiency of Tom and Avery is 1/2 +1/4 = 3/4 units/hr
Since they worked for 1 hour they completed 3/4 units of work and 1/4 units of work is left which is to be completed by Tom ( Since Avery left )
So Time taken by Tom to complete the remaining work will be 1/4/1/4 hours => 1*60 = 60 minutes...
Answer will be (D)
Answer: D
Question: A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?
Options:
A)8
B)7
C)12
D)9
E)none of the above
Rationale: Ans is A:
39 pounds --> 6 days
91 pounds --> x days
x = 91*6/39 = 14
the animal has already consumed food in 6 days so the the number of days for it's total consumption be 91 pounds is 14-6 = 8
Answer: A
Question: A football team lost 5 yards and then gained 9. What is the team's progress?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Solution
For lost, use negative. For gain, use positive.
Progress = -5 + 9 = 4 yards
Answer B
Answer: B
Question: A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or doubled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $40,000 in property taxes, but did not pay until October 15th?
Options:
A)$1,400
B)$1,800
C)$2,400
D)$3,200
E)$22,800
Rationale: Original amount = 40,000
Fine for July = 40,000 * 1% = 400
Fine for August = lesser of the 2 , 400+600= 1000 or 400*2=800 . Pick 800
Fine for September = 800+600=1400 or 800*2 = 1600. Pick 1600
Fine for October = 1600+600=2200 or 1600*2 = 3200. Pick 3200.
The wording of the question should be have been clearer as total fines should be = 3200+1600+800+400 = 6000 and NOT 3200.
3200 is the fine ONLY for the month of October!
D
Answer: D
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 19. Find the sum :
Options:
A)4500
B)7600
C)5000
D)6000
E)None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2100=10100×5×2100=10
and CI = 100(1+5100)2−100100(1+5100)2−100
∴ =100×21×2120×20−100=414=100×21×2120×20−100=414
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 19, the sum
= 400 × 19 = 7600 Answer B
Answer: B
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 160 six-ounce servings of orange juice?
Options:
A)20
B)24
C)28
D)32
E)36
Rationale: 1 X 12 ounce can of concentrate + 3 X 12 ounce cans of water = 48 ounces of the mixture.
48 ounces of mixture gives (48 / 6 ) = 8 servings.
Thus 1 x 12 ounce can of concentrate is used to produce 8 servings of the mixture.
To make 160 servings of the mixture, we need 160 / 8 = 20 cans of the concentrate.
The answer is A.
Answer: A
Question: Given A+B+C+D+E= FG. If FG is Maximum as possible and A,B,C,D,E,F,G all are distinct digits
(0-9) then what is the value of G.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: A+B+C+D+E=FG
9+8+7+6+5=35 Here E=G, So it is not possible.
again 9+8+7+6+4=34 Here also E=G, so it is also not possible
again 9+8+7+5+4=33 Here F=G
Finally 9+8+6+5+4=32 In this case condition is satisfies, so all are distinct and value of G=2.
ANSWER:B
Answer: B
Question: If p and q are prime numbers, how many divisors does the product p^3*q^6 have?
Options:
A)9
B)12
C)18
D)28
E)363
Rationale: , p^2, p^3 and q, q^1, q^2.... q^6 together
Essentially there are 18 different combinations you can make (3x6)
Also you have to include the different combinations the p and q exponents can be a divisor. There are 3 different p exponents and 6 different q exponents: p, p^2, p^3, q, q^2, q^3... q^6
Also add 1 since "1" can also be a divisor.
18+3+6+1 = 28 , ANSWER:D
Answer: D
Question: If a mixture is 3⁄5 alcohol by volume and 4⁄5 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
Options:
A)1/3
B)3/2
C)3/4
D)3
E)3/5
Rationale: Should be a sub-600 level Q..
volume= {3/5}/{4/5}=3/4
C
Answer: C
Question: At what rate percent of simple interest will a sum of money double itself in 66 years?
Options:
A)6.54 %
B)4.54 %
C)1.51 %
D)1.94 %
E)5.54 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 66)
= 100/66 = 1.51 %
ANSWER:C
Answer: C
Question: If |2x| = 50, what is the sumof all the possible values of x?
Options:
A)15
B)20
C)25
D)-25
E)0
Rationale: There will be two cases
2x = 50 or 2x = -50
=> x = 25 or x= -25
sum of both the values will be -25 +25 = 0
Answer is E
Answer: E
Question: By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is
Options:
A)25%
B)35%
C)20%
D)23%
E)30%
Rationale: Suppose S.P of 50 mangoes = Rs 50
Therefore, Gain = Rs 10 => C.P = Rs 40
Gain % = 10/40 x 100 = 25%
Gain = 25%
ANSWER:A
Answer: A
Question: How many three-digit numbers are there such that all three digits are different and the first digit is not zero?
Options:
A)504
B)648
C)720
D)729
E)810
Rationale: The first digit cannot be 0, so there are 9 options for the first digit.
the second digit can be any number (10 possibilities) but cannot be equal to the first digit. Therefore, there are (10-1) 9 possibilities for the 2nd digit.
The third digit can be any digit (10 possibilities) but cannot be equal to the first two digits. Therefore, there are (10-2) 8 possibilities for the 3rd digit.
So there are 9 * 9 * 8 = 648 possibilities.
ANSWER:B
Answer: B