mathewhe/aqua_rat huggingface dataset:
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
(A) 5
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
C
Answer: (C) 6
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 1/2M + 15, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?
(A) a.	A - 10
(B) b.	B - 15
(C) c.	C – 22.5
(D) d.	D – 30
(E) e.	E – 67.5
Rationale: A --- 10/2 + 15 = 20 --- CORRECT
B --- 15/2 + 15 = not an integer --- wrong
C --- 22.5(1/2) + 15 = not an integer --- wrong
D --- 30/2+15 =30 --- wrong
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
A
Answer: (A) a.	A - 10
Question: On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 16 miles on Saturday and Sunday, how many miles did Bill run on Sunday?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let Bill run x on saturday, so he will run x+4 on sunday..
Julia will run 2*(x+4) on sunday..
totai= x+x+4+2x+8=16..
4x+12=16..
x=1..
ans =x+4=1+4=5
Answer A
Answer: (A) 5
Question: In assembling a Bluetooth device, a factory uses one of two kinds of modules. One module costs $10 and the other one, that is cheaper, costs $3.5. The factory holds a $45 worth stock of 11 modules. How many of the modules in the stock are of the cheaper kind?
(A) 30
(B) 28
(C) 25
(D) 20
(E) 10
Rationale: So the number of $3.50 modules must be 10 so that the leftover 1 modules are of $10 which will give a total value $45. 10*3.50+1*10 = 35+10=45
Answer : E
Answer: (E) 10
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg, what is his percent?
(A) 25%
(B) 17%
(C) 29%
(D) 55%
(E) 45%
Rationale: 850 --- 150
100 --- ? => 17.64%
Answer: B
Answer: (B) 17%
Question: In how many ways the letters of the word TIME be arranged?
(A) 25
(B) 4
(C) 24
(D) 89
(E) 120
Rationale: Total ways of arranging the letters = 4! = 24 ways.
C)
Answer: (C) 24
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 48% nuts, what percent of the combined mixture is dried fruit?
(A) 20%
(B) 24%
(C) 28%
(D) 32%
(E) 36%
Rationale: 48% is 18%-points above 30% and 12%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 2:3.
2/5*70% = 28%
The answer is C.
Answer: (C) 28%
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 2 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
(A) 30
(B) 20
(C) 18
(D) 22
(E) 6
Rationale: 21-12 < no of hrs < 21-2
9< no of hrs < 19.
C
Answer: (C) 18
Question: If 3 tic equals 6 tacs and 2 tacs equal 7 tocs, what is the ratio of one tic to one toc?
(A) 7/1
(B) 6/5
(C) 5/6
(D) 3/10
(E) 1/15
Rationale: 3Tic=6*Tac and 2*Tac=7*Toc;
6*Tic=12*Tac and 12*Tac=42*Toc --> 6*Tic=42*Toc --> Tic/Toc=42/6=7/1.
Answer: A.
Answer: (A) 7/1
Question: The total marks obtained by a student in Mathematics and Physics is 80 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 30
(C) 25
(D) 50
(E) None of these.
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 80 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (80 + 20) / 2 = 50.
ANSWER:D
Answer: (D) 50
Question: A woman can do a piece of work in 40 days. Man is 25% more efficient than Woman. In how many days a man can do the same piece of work?
(A) 32 days
(B) 36 days
(C) 38 days
(D) 40 days
(E) 53 days
Rationale: The ratio of the efficiencies of a woman and man = 100 : 125
= 4 : 5
The ratio of the days taken by woman and man to finish the work = 5 :4
Woman takes 32 days to finish the work.=> 5 parts = 40
The number of days taken by man to finish the work = 4 parts = 40/5x 4 = 32 days
A
Answer: (A) 32 days
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 10 years
(D) 12 years
(E) None of these
Rationale: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20 => x = 4.
Age of youngest child = x = 4 years.
ANSWER:A
Answer: (A) 4 years
Question: How long will a boy take to run round a square field of side 60 meters, if he runs at the rate of 9km/hr?
(A) 96sec
(B) 45sec
(C) 1min
(D) 32sec
(E) 25sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 60*4 = 240m
Time taken = 240*2/5 = 96sec
Answer is A
Answer: (A) 96sec
Question: Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) 20,000
(B) 20,007
(C) 20,005
(D) 20,002
(E) 20,001
Rationale: Let the second amount be Rs. x. Then,
(12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100
120000 + 20x = 16800 + 14x
x = 8000
Total investment = 12000 + 8000 = Rs. 20,000.Answer: A
Answer: (A) 20,000
Question: How many cubes of 10 cm edge can be put in a cubical box of 1 m edge.
(A) 10000 cubes
(B) 1000 cubes
(C) 100 cubes
(D) 50 cubes
(E) None of these
Rationale: Explanation:
Number of cubes =100∗100∗100 /10∗10∗10=1000
Note: 1 m = 100 cm
Option B
Answer: (B) 1000 cubes
Question: 15.03 Ã— 0.01 = ?
(A) 0.1503
(B) 0.001503
(C) 1.503
(D) 0.001503
(E) None of these
Rationale: 15.03 Ã— 0.01 = ?
or,? = 0.1503
Answer A
Answer: (A) 0.1503
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 35 cm?
(A) 276 sq.cm
(B) 268 sq.cm
(C) 618 sq.cm
(D) 297 sq.cm
(E) 700 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 * 35
= 700 sq.cm.
Answer:E
Answer: (E) 700 sq.cm
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2/1
(B) 4/1
(C) 2/3
(D) 3/4
(E) 3/1
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+3) = 36/12 = 3/1.
Answer: E.
Answer: (E) 3/1
Question: Tough and Tricky questions: Ratios
1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
(A) 1/2
(B) 2/3
(C) 7/15
(D) 23/30
(E) 4/5
Rationale: let total no. of students be 30
students left on a field trip = 1/5(30) =6
thus 24 students left behind
1/3(24)=8 students did not want to go. thus 16 students want to go on the trip
1/2(16)=8 were able to join the other students on the field trip.
thus total number of students that went on a field trip =6+8 =14
thus required fraction = 14/30 =7/15
C
Answer: (C) 7/15
Question: The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?
(A) 37 kg
(B) 35 kg
(C) 85 kg
(D) 45 kg
(E) 25 kg
Rationale: 7/20 * 100 = 35
Answer: B
Answer: (B) 35 kg
Question: The sum and the product of the roots of the quadratic equation x2 + 20x + 3 = 0 are?
(A) 10, 3
(B) -10, 3
(C) 20,-3
(D) -10,-3
(E) None of these
Rationale: Explanation:
Sum of the roots and the product of the roots are -20 and 3 respectively.
ANSWER IS E
Answer: (E) None of these
Question: John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $55. What is the percent decrease?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 45%
Rationale: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 55 = 45. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (45/100)*100 = (0.45)*100 = 45%.
E
Answer: (E) 45%
Question: The triplicate ratio of 1:2 is?
(A) 1:7
(B) 1:8
(C) 1:3
(D) 1:1
(E) 1:2
Rationale: 13: 23 = 1:8
Answer: B
Answer: (B) 1:8
Question: A certain gallery is hanging a series of 7 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 3 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
(A) 240
(B) 200
(C) 144
(D) 80
(E) 16
Rationale: We need to consider them separately because the question specifies:
1. Panel paintings have to be placed only at 2nd, 3nd and 6th place.
2. Implies that Canvas has to be placed 1,4,5,7th place.
So we have two separatebucketsto consider.
So panels can be ordered in 3!
Canvas can be ordered in 4!
since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 3! x 4! = 144
C
Answer: (C) 144
Question: The average age of 28 students in a group is 11 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
(A) 36
(B) 38
(C) 40
(D) cannot be determined
(E) None of these
Rationale: Age of the teacher = (29 × 12 – 28 × 11) years
= 40 years.
Answer C
Answer: (C) 40
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 630meters, after what time will they meet at the starting point?
(A) 20sec
(B) 15sec
(C) 42sec
(D) 50sec
(E) 1min
Rationale: They meet every 630/7+8 = 42sec
Answer is C
Answer: (C) 42sec
Question: Average between two sets of numbers is closer to the set withmore numbers?
(A) 60
(B) 80
(C) 98
(D) 89
(E) 91
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: (B) 80
Question: If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?
(A) 4%
(B) 10%
(C) 14%
(D) 15%
(E) 18%
Rationale: Let Cost of PROD for 1 ticket = 1
So COP for n tickets = n
So for selling n tickets, SP = 1.2 * n = 1.2n
So SP of 1 ticket = 1.2
SP of 95% tickets = 1.2 * 0.95n
So profit % = (1.2 * 0.95n - n)/n * 100
= 0.14 * 100
= 14%
Answer - C
Answer: (C) 14%
Question: How many possible ways are there to select 2 stocks at random from 7 stocks?
(A) 17
(B) 19
(C) 21
(D) 23
(E) 25
Rationale: 7C2 = 21
The answer is C.
Answer: (C) 21
Question: A 6% stock yields 8%. The market value of the stock is
(A) 33
(B) 75
(C) 44
(D) 27
(E) 91
Rationale: For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs. 100	x 6 = Rs. 75.
8
Market value of Rs. 100 stock = Rs. 75.
Answer: B
Answer: (B) 75
Question: Which of the following number is divisible by 24 ?
(A) 35718
(B) 63810
(C) 537804
(D) 3125736
(E) 63811
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
Answer:D
Answer: (D) 3125736
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 54 seconds. The length of each train is:
(A) 82m
(B) 50m
(C) 75m
(D) 80m
(E) None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 54 secs the total distance traveled is 54x25/9 = 150 m.
Therefore the length of each train is = 150/2 = 75 m.
Answer C
Answer: (C) 75m
Question: An article is bought for Rs.1200 and sold for Rs.1300, find the loss percent?
(A) 8.33%
(B) 9.33%
(C) 10.00%
(D) 11.11%
(E) 7.56%
Rationale: 1200 ---- 100
100 ---- ? => 16 2/3%
Answer: A
Answer: (A) 8.33%
Question: If the number 53,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
(A) 7
(B) 5
(C) 2
(D) 1
(E) 0
Rationale: The sum of the digits 5 + 3 + 1 + n + 9 must be a multiple of 3
18 + n must be a multiple of 3
substituting the numbers n must = 0
Answer E
Answer: (E) 0
Question: A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places?
(A) 3/100
(B) 3/5
(C) 1/100
(D) 1/4,900
(E) 1/5
Rationale: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300
Number CA possible = 1C1 = 1
Number FL possible = 1C1 = 1
Number HI possible = 1C1 = 1
Number other possible = 47C1 = 47
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900
Answer: D
Answer: (D) 1/4,900
Question: The mean of four integers E will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: (A) I only
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 1
(E) 2
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 324. Hourly wage = 324 / 36 = 9
Answer: C) 9
Answer: (C) 9
Question: The number 4 is the smallest positive
integer that has exactly three factors:
1, 2, and 4. If k is the next-highest integer
that also has exactly three factors, what is
the sum of the three factors of k?
(A) 20
(B) 18
(C) 16
(D) 14
(E) 13
Rationale: The greatest of the five possible answers is 20, so k is less than 20. Use trial and error to
find the value of k:
Factors of 5: 1 5
Factors of 6: 1 2 3 6
Factors of 7: 1 7
Factors of 8: 1 2 4 8
Factors of 9: 1 3 9
Thus, k = 9, and the sum of the factors of k is 1 + 3 + 9 = 13.
correct answer E)13
Answer: (E) 13
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 16.98%
(D) 17.23%
(E) 18.3%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: What is 0.01 percent of 15,356?
(A) 0.15356
(B) 1.5356
(C) 15.356
(D) 0.015356
(E) 0.0015356
Rationale: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.01(1/100)15,356. The answer is 1.5356. Hence, the correct answer is B.
Answer: (B) 1.5356
Question: Two taps can separately fill a cistern 20 minutes and 30 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 38
(B) 37
(C) 36
(D) 39
(E) 35
Rationale: 1/20 + 1/30 - 1/x = 1/18
x = 36
Answer:C
Answer: (C) 36
Question: If (8,000)(6,000) = (480)(10^y), what is the value of y?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: (8,000)(6,000) = (480)(10^y)
=> (8,000)(6,000)/480 = 10^y
=> 100,000 = 100^y
=> 10^5 = 10^y
Since, base is same so powers will be same too.
So, y=5
Answer will be A
Answer: (A) 5
Question: The sum of two numbers is 16. The difference is 6. What are the two numbers?
(A) 10-6
(B) 8-8
(C) 9-7
(D) 11-5
(E) 13-3
Rationale: 11+5 = 16
11 - 5 = 6
The Answer is D
Answer: (D) 11-5
Question: Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?
(A) 12 pm
(B) 1 pm
(C) 2 pm
(D) 3 pm
(E) 4 pm
Rationale: Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the Printer were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
B
Answer: (B) 1 pm
Question: Paul buys his co-workers donuts 24 glazed, 12 creme-filled and 6 with sprinkles. The glazed donuts cost $0.75 each, the creme-filled donuts cost $1.00 each, and the sprinkle covered donuts cost $0.50 each. What is the average cost Paul paid for each donut?
(A) 70 cents
(B) 75 cents
(C) 79 cents
(D) 80 cents
(E) 1 dollar
Rationale: Explanation:
24 12 6
0.75 1.00 0.50
$18 + $12 + $3 = $33/42 = $0.79
C
Answer: (C) 79 cents
Question: How many positive integers less than 100 have a remainder of 6 when divided by 13?
(A) 2
(B) 7
(C) 6
(D) 9
(E) 10
Rationale: We have to include 6 also.As 13*0 + 6 =6
If somebody says to divide 6 by 13 ,we will be telling we have 0 quotient and remainder as 6.
Answer is C
Answer: (C) 6
Question: If the price of a certain computer increased 30 percent from d dollars to 377 dollars, then 2d =
(A) 540
(B) 570
(C) 619
(D) 649
(E) 580
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(30/100)*D = 1.3d = 377 (Given)
i.e. d = 377/1.3 = $290
i.e. 2d = 2*290 = 580
Answer: option E
Answer: (E) 580
Question: For any number x, x* is defined as the greatest positive even integer less than or equal to x. What is the value of 5.2 – 5.2*?
(A) 0.2
(B) 1.2
(C) 1.8
(D) 2.2
(E) 4.0
Rationale: Since x* is defined as the greatest positive even integer less than or equal to x, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: (B) 1.2
Question: The compound ratio of 5:6, 3:2 and 4:5?
(A) 1:8
(B) 1:6
(C) 1:2
(D) 1:1
(E) 1:7
Rationale: 5/6 * 3/2 * 4/5
= 1/1
1:1
Answer: D
Answer: (D) 1:1
Question: The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 40% alcohol, is?
(A) 2.25
(B) 4.25
(C) 5.25
(D) 6.25
(E) 7.25
Rationale: 4.5 4.5
40% 60%
40% ----- 4.5
60% ------? => 6.75 - 4.5 = 2.25 ml
ANSWER:A
Answer: (A) 2.25
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 180
(B) 128
(C) 276
(D) 297
(E) 236
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Answer: (A) 180
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum Q of all possible 2-digit remainders for x/y?
(A) 560
(B) 616
(C) 672
(D) 728
(E) 784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
Q=8(2+3+4....+12)=616
Answer: (B) 616
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 6x km.
(A) 40kmph
(B) 45kmph
(C) 48kmph
(D) 50kmph
(E) 55kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 6x/(x/8)
= 48 kmph
Answer:C
Answer: (C) 48kmph
Question: If a#b = ab – b + b^2, then 3#8 =
(A) 80
(B) 8
(C) 15
(D) 21
(E) 35
Rationale: Solution -
Simply substitute 3 and 8 in equation in the place of a and b respectively.
3#8 = 3*8 - 8 + 8^2 = 24 - 8 + 64 = 80. ANS A
Answer: (A) 80
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
(A) 76
(B) 28
(C) 26
(D) 20
(E) 27
Rationale: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is
= 28
Answer:B
Answer: (B) 28
Question: A survey is conducted on 800 people from a city. It is found that 6 1% of people surveyed speakHindi, 54.5% people speak Bangla and 37.5% of them speak English. 16.5% people can speak only Hindi and Bangla, 14.5% people can speak only Hindi and English and 6% people can speak only Bangla and English. Answer the following questions based on this information.
How many people are there who can speak only Hindi ?
(A) 172
(B) 174
(C) 176
(D) 178
(E) 179
Rationale: Explanation :
x + y + z + k = 800 - (132 + 116 + 48) = 504 .....(i)
x + k = 488 - (132 + 116) = 240 .....(ii)
y + k = 436 - (132 + 48) = 256 ......(iii)
z + k = 300 - (116 + 48) = 136 .....(iv)
(eqn ll + lll + IV) - eqn (l) gives
2k = (240 + 256 + 136) - 504
2k = 632 - 504 = 128 ∴ k = 64
x = 240 - 64 = 176
y = 256 - 64 = 192
z = 136 - 64 = 72
Answer : Option C
Answer: (C) 176
Question: An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 36 coaches are attached.
(A) 24
(B) 28
(C) 20
(D) 32
(E) 40
Rationale: 1.
No. of coaches =4
sqr root=2
speed decreases by 12
12=k*2
k=6
No. of coaches=36
swr root=6
decrease=6*6=36
New speed=60-36=24
A
Answer: (A) 24
Question: Divide 5679 by 7 and find out remainder and quotient ?
(A) 901, 5
(B) 811, 2
(C) 921, 7
(D) 805, 4
(E) 951, 20
Rationale: dividend = divisor * quotient + remainder ===> 5679 = 7 * 811 + 2 ===> remainder = 2 and quot = 811 Ans - B
Answer: (B) 811, 2