mathewhe/aqua_rat huggingface dataset:
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?
(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) 1
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?
(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) 13 hrs
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?
(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) 12.5% profit
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?
(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) 82
Question: On 6th July, 2017 Thursday falls. What day of the week was it on 6th July, 2016?
(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) Wednesday
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?
(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) 20
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
(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) 12.26%
Question: At 15:15 pm railway time, what will be the angle between minute and hour hand?
(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) 360
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.
(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) s. 50
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 ?
(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) 7/9
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?
(A) 300
(B) 250
(C) 130
(D) 303
(E) 111
Rationale: 830-527=303. Answer is D.
Answer: (D) 303
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?
(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) 20
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?
(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) 16.5
Question: There are 6 people and 3chairs. In how many ways people can occupy the chairs?
(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) 120
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
(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) 9.6
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?
(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) 64*3^1/3
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?
(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) Rs.250
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?
(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) 39.
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?
(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)  $600
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?
(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) E)25
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?
(A) 44%
(B) 49%
(C) 84%
(D) 24%
(E) 45%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: A
Answer: (A) 44%
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?
(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) 60
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?
(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) 8
Question: A football team lost 5 yards and then gained 9. What is the team's progress?
(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) 4
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?
(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) $3,200
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 :
(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) 7600
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?
(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) 20
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.
(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) 2
Question: If p and q are prime numbers, how many divisors does the product p^3*q^6 have?
(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) 28
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?
(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) 3/4
Question: At what rate percent of simple interest will a sum of money double itself in 66 years?
(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) 1.51 %
Question: If |2x| = 50, what is the sumof all the possible values of x?
(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) 0
Question: By selling 50 mangoes, a shopkeeper gains the price of 10 mangoes. His gain per cent is
(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) 25%
Question: How many three-digit numbers are there such that all three digits are different and the first digit is not zero?
(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) 648
Question: A car is traveling at uniform speed. The driver sees a milestone showing a two digit number which is a perfect square, after traveling for an hour the driver sees another milestone with the same digits in reverse order and after another hour the driver sees another milestone containing the same two digits as part of a three digit number. What is the speed of the car?
(A) 30 kmph
(B) 40 kmph
(C) 50 kmph
(D) 60 kmph
(E) 45 kmph
Rationale: first milestone driver see is 16,second is 61,&third is 106.
so total distance traveled by him=106-16=90km
time taken=2h
so speed=distance/time=90/2=45kmph
ANSWER:E
Answer: (E) 45 kmph
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 4
III. ab is even
(A) I only
(B) III only
(C) I and II
(D) I and III
(E) I, II, and III
Rationale: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
III only.letter B
Answer: (B) III only
Question: 4^b + 4^b + 4^b + 4^b =
(A) 7^b
(B) 4^(b + 1)
(C) 7^(7b)
(D) 8^b
(E) 49^B
Rationale: Easy one.
4*4^b = 4^(b+1)
Ans. B
Answer: (B) 4^(b + 1)
Question: A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 10 hours. During that time, the faster car traveled 2/3 of the distance XY. How long would it take the slower car to travel the distance XY?
(A) 6 hours
(B) 8 hours
(C) 30 hours
(D) 12 hours
(E) 15 hours
Rationale: If one car travelled 2/3, then the other car must have travelled only 1/3, as they are meeting after 10 hours in a certain point. So:
(1/3)XY= 10*y --> It took the car 10 hours to travel 1/3 of the distance at a constant speed y.
So if we solve this last equation:
XY= 3*10*y= 30*y --> It will take this car 30 hours in total to reach its final destination.
Answer: C
Answer: (C) 30 hours
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 5 and 7 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
(A) Per month, with savings of $(4a + 4b)
(B) Per month, with savings of $(4a - 4b)
(C) The two options would cost an equal amount.
(D) Per project, with savings of $(4a + 4b)
(E) Per project, with savings of $(4a - 4b)
Rationale: Per Project, company will pay as follows:
For 5 hours work = a+4b
For 7 hours work = a+6b
Total = 2a+10b
Per Month, company will pay for 12 hours work = a+11b
Total per contract - total per month
5a+7b - (a+11b)
4a-4b
Since a>b Amount 5a+7b(per contract amount) > a+11b (per project amount) by 4a-4b.
Hence per month payment will be cheaper by 4a-4b .
OA B
Answer: (B) Per month, with savings of $(4a - 4b)
Question: 15 - 2 + 4 ÷ 1/2 × 8 = ?
(A) 272
(B) 77
(C) 168
(D) 56
(E) 59
Rationale: Explanation:
15 - 2 + 4 ÷ 1/2 × 8 = 15 - 2 + 4 × 2 × 8 = 15 - 2 + 64 = 77
Answer: Option B
Answer: (B) 77
Question: What is the least value of x. So that 21x57 is divisible by 3.
(A) 2
(B) 0
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 1 + x + 5 + 7 = 15 + x
Least value of x may be 0
Therefore 15 + 0 = 15 is divisible by 3.
Answer: Option B
Answer: (B) 0
Question: Pipe A can fill a tank in 20 Mins and pipe B can fill it in 30 Mins. If both the pipes are opened in the empty tank. In how many Mins will it be fill exact half of the tank?
(A) 4 mins
(B) 5 mins
(C) 6 mins
(D) 7 mins
(E) 8 mins
Rationale: Part filled A in 1 hr= (1/20)
Part filled B in 1 hr= (1/30)
Part filled by (A+B) together in 1 hr=(1/20)+(1/30)=1/12
So, The tank will be full in 12 mins
Time taken to fill Exact half tank = 12/2 = 6 Mins.
Answer : C
Answer: (C) 6 mins
Question: The area of playground is 5800 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
(A) a) $144
(B) b) $150.50
(C) c) $162
(D) d) $158.60
(E) e) $160.70
Rationale: total volume * unit cost = total cost
or, 5800 * 0.01 * 2.8 = total cost = 162=C
Answer: (C) c) $162
Question: A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $75000 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
(A) 5
(B) 6
(C) 9
(D) 10
(E) 15
Rationale: Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x
Gievn: Total $1250 scholarships = $75000
6x*1250 = 75000
Solve for x = 10
Option D
Answer: (D) 10
Question: A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
(A) 60km/hr
(B) 54km/hr
(C) 50km/hr
(D) 45km/hr
(E) 62km/hr
Rationale: Number of gaps between 21 telephone posts = 20
distance travelled in 1 minute = 50*20 = 1000m = 1km
speed = 60km/hr
Answer is A
Answer: (A) 60km/hr
Question: Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?
(A) 3
(B) 3.3
(C) 3.5
(D) 3.6
(E) None
Rationale: Explanation: In this simple subtraction series, each number decreases by 0.4.
Answer: Option D
Answer: (D) 3.6
Question: A tempo is insured to an extent of 4/5 of its original value. If the premium on it at the rate of 1.3% amounts to $910, The original value of the tempo is?
(A) 92500
(B) 75230
(C) 65990
(D) 45280
(E) 87500
Rationale: Let the original value of the tempo is $x
1.3% of 4/5 of x = 910
(13/10)*(1/100)*(4/5)x = 910
x = $ 87500
Answer is E
Answer: (E) 87500
Question: If -3x < 0, which of the following must be true?
(A) x < -3
(B) x < -2
(C) x > 3
(D) x > -2
(E) x > 0
Rationale: -3x < 0
=> -x < 0
=> x > 0
Answer E
Answer: (E) x > 0
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 27
(B) 89
(C) 29
(D) 20
(E) 22
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer:B
Answer: (B) 89
Question: #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=-4?
(A) –108
(B) –44
(C) 10
(D) -18
(E) 18
Rationale: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = -4 ---> 8p= -144 ---> p = -18, D is the correct answer.
Answer: (D) -18
Question: When x - p is divided by p - 2, the quotient is n and there is no remainder. Which of the following must be the value of x?
(A) n(p +1)
(B) n(p − 1)
(C) p(n + 1) + 2n
(D) p(n - 1) + n
(E) n(p + 1) (p − 1)
Rationale: Given in question (x-p)/p-2= n
=> x-p= n(p-2)
=>x= np+2n+p
or x= np+p+2n
Now we are good to check the options
x= p(n+1) + 2n
Answer C
Answer: (C) p(n + 1) + 2n
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1345
(C) 1455
(D) 1577
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: A group of people participate in some curriculum, 25 of them practice Yoga, 15 study cooking, 8 study weaving, 2 of them study cooking only, 7 of them study both the cooking and yoga, 3 of them participate all curriculums. How many people study both cooking and weaving?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Both cooking and weaving = 15 - (2+3+7) = 3
So, the correct answer is C.
Answer: (C) 3
Question: A walks at 30 kmph and 30 hours after his start, B cycles after him at 50 kmph. How far from the start does B catch up with A?
(A) 1200km
(B) 1500km
(C) 2000km
(D) 2250km
(E) 3600km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.
x/30 - x/50 = 30
x = 2250 km
Answer is D
Answer: (D) 2250km