mathewhe/aqua_rat huggingface dataset:
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 7 kmph
(B) 4 kmph
(C) 4 kmph
(D) 8 kmph
(E) 5 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer: D
Answer: (D) 8 kmph
Question: Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
(A) 9/25
(B) 9/50
(C) 18/25
(D) 20/25
(E) 15/25
Rationale: Solution:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25
ANSWER IS A
Answer: (A) 9/25
Question: Jacob's age 18 years hence will be thrice his age four years ago. Find Jacob's present age?
(A) 16
(B) 20
(C) 15
(D) 11
(E) 16
Rationale: C
15
Let Jacob's present age be 'm' years.
m + 18 = 3(m - 4)
=> 2m = 30 => m = 15 years.
Answer: (C) 15
Question: Tough and Tricky questions: Exponents.
If 3^m3^m3^m = 6^n, then m/n =
(A) 1/3
(B) 2/3
(C) 1
(D) 3/2
(E) 3
Rationale: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!
What I did was to test powers of 3 that would lead to 9.
So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n
What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=3.E
Answer: (E) 3
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 6400 a year. What is his average monthly income?
(A) 2000
(B) 2010
(C) 2100
(D) 2200
(E) 2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 6400 = Rs. 26400
So, Average monthly income = 26400/12 = Rs. 2200
D
Answer: (D) 2200
Question: The ratio of two numbers is 5:6. If a number is added to both the numbers the ratio becomes 7:8. If the larger number exceeds the smaller number by 10. Find the number added.
(A) 30
(B) 10
(C) 20
(D) 40
(E) Cannot be determined
Rationale: let the numbers are 5x and 6x. Let the number added is y so 5x+y/6x+y = 7/8
and 6x-5x = 10 implies x = 10
taking x=10, 50+y/60+y = 7/8 implies 400+8y = 420+7y or y = 20
ANSWER:C
Answer: (C) 20
Question: If the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is?
(A) 11
(B) 14
(C) 16
(D) 12
(E) 19
Rationale: 2 * 22/7 * 12 * x = 1240=> x = 16
Answer: C
Answer: (C) 16
Question: Jane covered a distance of 350 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 3 hours 30 minutes
(B) 3 hours
(C) 2 hours
(D) 1 hour 45 minutes
(E) None of these
Rationale: Answer
Let Jane travel 'x' at 60 miles per hour.
As the total time taken to cover 340 miles is 5 hours, Jane would have traveled (5 - x) hours at 80 miles per hour.
Distance covered at 60 miles per hour = Speed * time = 60 * x = 60x miles.
Distance covered at 80 miles per hour = Speed * time = 80 (5 - x) = 400 - 80x miles.
Total distance covered = Distance covered at 60 miles per hour + Distance covered at 80 miles per hour.
Therefore, total distance = 60x + 400 - 80x.
Total distance travelled = 340 miles.
Therefore, 350 = 60x + 400 - 80x
20x = 70 or x = 3 hours 30 minutes.
Choice A
Answer: (A) 3 hours 30 minutes
Question: Sachin is younger than Robert by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
(A) 24.5
(B) 32
(C) 25
(D) 28
(E) 30
Rationale: Let Robert's age be x years
Then sachin's age = x-7 years
(x-7)/x = 7/9
x = 31.5
Sachin's age = x-7 = 24.5 years
Answer is A
Answer: (A) 24.5
Question: ICICI bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
(A) 1:5
(B) 625:3125
(C) 100:105
(D) 100^4:105^4
(E) 725:3225
Rationale: Hi Bunuel,
Here is my approach: is this correct?
ICICI bank offers an interest of 5% per annum compounded annually on all its deposits.
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Answer: (C) 100:105
Question: The profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
(A) 960
(B) 975
(C) 1,200
(D) 920
(E) None of these
Rationale: Let the profit or loss be x
and 852 – x = 448 + x or, x = 404⁄2 = 202
\ Cost price of the article = 852 – x = 448 + x = 650
\ SP of the article = 650 × 150⁄100 = 975
Answer B
Answer: (B) 975
Question: 16 grams of radioactive material decays into 8 grams in 10 years. How long will it take to decay to 1 gram?
(A) 30 years
(B) 42 years
(C) 45 years
(D) 40 years
(E) 50 years
Rationale: This radioactive material has half life after 10 years.
16 grams decays into 8 grams in 10 years.
Then 8 grams decays into 4 grams in next 10 years.
Then 4 grams decays into 2 grams in next 10 years.
Then 2 grams decays into 1 gram in next 10 years.
Thus 16 grams decays into 1 gram in 40 years.
ANSWER:D
Answer: (D) 40 years
Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.
(A) 10 seconds
(B) 12 seconds
(C) 14 seconds
(D) 16 seconds
(E) 18 seconds
Rationale: Explanation:
As we need to get answer in seconds, so never forget to convert speed into meter per second.
Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec
Distance = length of train = 100 meter
Required time =
Distance/Speed=100 /25/3
=100∗3/25=12sec
Option B
Answer: (B) 12 seconds
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 9 3/7 days
(B) 9 7/8 days
(C) 9 3/8 days
(D) 4 3/8 days
(E) 9 6/8 days
Rationale: 1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Answer: C
Answer: (C) 9 3/8 days
Question: Two distinct numbers a and b are chosen randomly from the set of first 20 positive integers. What is the probability that |a–b| would not be divisible by 3?
(A) 49/380
(B) 21/95
(C) 49/190
(D) 42/95
(E) 133/190
Rationale: Any number could be written in the form of one among the following:
(i) 3k
(ii) 3k + 1
(iii) 3k + 2
Only if the 2 numbers are of different types would |a – b| not be divisible by 3:
Numbers of type 3k --> 3, 6, 9, ......... 18 --> Total 6 numbers
Numbers of type 3k + 1 --> 1, 4, 7, .... 19 --> Total 7 numbers
Numbers of type 3k + 2 --> 2, 5, 8, 11 ...20 -->Total 7 numbers
Total possible outcomes = 20 * 19 = 380
Favorable Cases:
1) Picking from Type 1 and Type 2: 2 * (6 * 7) = 84
2) Picking from Type 1 and Type 3: 2 * (6 * 7) = 84
3) Picking from Type 2 and Type 3: 2 * (7 * 7) = 98
Hence, the required probability = (84 + 84 + 98) / 380, and E is the correct answer.
Answer: (E) 133/190
Question: Charan can do a piece o work in 24 days, which Hari alone can finish in 19 days. Both together work for 7 days and then Hari leaves off. How many days will Caran take to finish remaining work?
(A) 22days
(B) 22 ½ days
(C) 21 ½ days
(D) 20days
(E) 15 days
Rationale: Explanation:
Caran and Hari 7 days work = 7(1/24+1/19) = 43/456
Remaining work = (1- 43/456) =413/456
Charan 1 days work = 1/24
413/456 work will be done by Caran in 24* 413/456 = 22 days (approx)
Answer: Option A
Answer: (A) 22days
Question: If 10 men and 2 boys working together, can do nine times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 7:5
(B) 7:3
(C) 7:8
(D) 7:1
(E) 7:2
Rationale: 10M + 2B = 9(1M + 1B)
10M + 2B = 9M + 9B
1M = 7B
The required ratio of work done by a man and a boy = 7:1
Answer:D
Answer: (D) 7:1
Question: Mira’s expenditure and sayings are in the ratio 3: 2. Her income increases by 10 percent. Her expenditure also increases by 12 percent. By how much per cent does her saving increase?
(A) 7%
(B) 10%
(C) 9%
(D) 13%
(E) 15%
Rationale: We get two values of x ,7 and 13.
But to get a viable answer we must keep in mind that the central value(10)must lie between x and 12.
Thus the value of x should be 7 and not 13
Thus, Required %increase = 7%
ANSWER:A
Answer: (A) 7%
Question: Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,700 at the end of nine years, how much money did he borrow?
(A) 10,315
(B) 12,315
(C) 14,000
(D) 16,000
(E) 16,315
Rationale: Let the sum borrowed be x. Then,
(x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11700
⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11700
⇒ x = (11700×100/95)= 12315
Hence, sum borrowed = 12,315
Answer B
Answer: (B) 12,315
Question: A will was written such that an estate would be divided among four beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $40,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the four beneficiaries?
(A) $12436
(B) $13344
(C) $71234
(D) $15736
(E) $19403
Rationale: 1st - 40,000.
2nd - 0.8*40,000 = 32,000
3rd - 0.8*32,000 = 25,600
4th - 0.8*25,600 = ~20,480
Range = 40,000 - 20,480 = 19520
Answer: E.
Answer: (E) $19403
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 6000
(B) Rs. 7000
(C) Rs. 8800
(D) Rs. 9000
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 1/5 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
(A) 3/19
(B) 5/16
(C) 3/11
(D) 3/10
(E) 3/14
Rationale: Let Veena paid x,
so Akshitha paid x/5 , and Lasya paid 2x,
So total bill paid is given by
x+(x/5) +2x = 1, we get
i.e. x = 5/16
Answer: B
Answer: (B) 5/16
Question: A box contains three red marbles and 1 green marble. If the marbles are removed from the box one at a time, in random order, what is the probability that all three red marbles are removed before the green marble?
(A) 1/64
(B) 1/24
(C) 1/12
(D) 1/4
(E) 1/2
Rationale: There are 3 red marbles and 4 marbles total, so the probability of drawing a red marble on the first draw is 3/4 . On the second draw there are 2 red marbles and three marbles total so the probability of drawing a red marble is 2/3. On the third draw, there is only one red marble and one green marble, so the probability of drawing the red marble is 1/2. The probability of all three events happening is the product of the probabilities,3/4∗2/3∗1/2 or1/4
Answer D
Answer: (D) 1/4
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 70% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A)  7/12
(B)  1/4
(C)  1/2
(D)  7/24
(E)  17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
E
Answer: (E)  17/24
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 30 years older than Ayush who is 10 years old. At what age did the father get married ?
(A) 30years
(B) 31years
(C) 32years
(D) 33years
(E) 34years
Rationale: Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 30) years = 40 years.
Ayush's father's present age = (40 + 5) years = 45 years.
Ayush's father's age at the time of Ayush's birth = (45 - 10) years = 35 years.
Therefore Ayush's father's age at the time of marriage = (35 - 2) years = 33 years.
Answer: D) 33 year
Answer: (D) 33years
Question: Find the cost of fencing around a circular field of diameter 22 m at the rate of Rs.2.50 a meter?
(A) 188
(B) 172
(C) 278
(D) 279
(E) 222
Rationale: 2 * 22/7 * 11 = 69
69 * 2 1/2
= Rs.172
Answer: B
Answer: (B) 172
Question: Rs. 1000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/2:1/4?
(A) 200
(B) 992
(C) 772
(D) 552
(E) 312
Rationale: 1/2:1/2:1/4 = 2:2:1
1/5*1000 = 200
400-200 = 200
Answer: A
Answer: (A) 200
Question: If K is the sum of reciprocals of the consecutive integers from 23 to 28, inclusive, then K is closest in value to which of the following?
(A) 1/12
(B) 1/10
(C) 3/14
(D) 1/8
(E) 1/4
Rationale: 1/23 , 1/24 , 1/25 , 1/26 , 1/27 , 1/28
Hypothetically , assume all 6 Numbers to be 1/23
Hence sum of it would result in = 6/23 ( almost equals 1/4 , or slightly more than 1/4 - )
If all 6 nos were to be 1/28 ... Sum of which would result in 6/28 = 3/14 .
Hence answer should lie between 1/4 and 3/14
i.e 0.25 > 0.21
C
Answer: (C) 3/14
Question: An Air Cooler is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
(A) 18%
(B) 19%
(C) 21.2%
(D) 21.81%
(E) 22.07%
Rationale: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: Air Cooler on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Answer: (D) 21.81%
Question: The average age of a committee of 12 members is 40 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
(A) 38.7 years
(B) 38 years
(C) 36 years
(D) 35 years
(E) 34 years
Rationale: Exp. Total age of the committee = 40*12 = 480,
Total age when a member is retired
and a new one was joined = 480-55 +39, =464
Average age of present committee = 464/12 = 38.7.
Answer: A
Answer: (A) 38.7 years
Question: The average mark obtained by 22 candidates in an examination is 48. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
(A) 22
(B) 0
(C) 49
(D) 58
(E) 66
Rationale: It is clear that 22 x 48 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 66
Answer:E
Answer: (E) 66
Question: What is the probability of flipping a fair coin eight times and the coin landing on heads on at least two flips?
(A) 61/64
(B) 117/128
(C) 123/128
(D) 247/256
(E) 253/256
Rationale: The number of possible outcomes is 2^8=256.
0 heads: There is 1 way to have all tails.
1 head: There are 8 ways to have one head.
P(0 or 1 head)=9/256
P(at least 2 heads)=1 - 9/256 = 247/256
The answer is D.
Answer: (D) 247/256
Question: six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15 ways
Rationale: 6c2 then ans is 6*5/1*2=15
ANSWER:E
Answer: (E) 15 ways
Question: A radio station has to choose five days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any five of the seven weekdays can be chosen. How many different five-day combinations of the seven weekdays can be constructed?
(A) 9
(B) 15
(C) 21
(D) 56
(E) 35
Rationale: Pick 5 days out of 7.. 7C5 = = 21
Answer : C
Answer: (C) 21
Question: 14 men can complete a piece of work in 22 days. In how many days can 18 men complete that piece of work?
(A) 23 days
(B) 26 days
(C) 17 days
(D) 29 days
(E) 20 days
Rationale: C
17 days
14 * 22 = 18 * x => x = 17 days
Answer: (C) 17 days
Question: If the complement of a certain angle is four times the measure of that certain angle, then what is the measure of that certain angle?
(A) 45°
(B) 30°
(C) 22.5°
(D) 18°
(E) 15°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 4x, and together, these add up to 90 degrees.
x + 4x = 90
5x = 90
x = 18°
Answer = (D)
Answer: (D) 18°
Question: Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1.5. Which of the following operations would decrease the standard deviation of Set J?
(A) Multiply each term by e/d
(B) Divide each term by b/c
(C) Multiply each term by −1
(D) Divide each term by a/e
(E) Multiply each term by c/e
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
D
Answer: (D) Divide each term by a/e
Question: The measurement of a rectangular box with lid is 25cmx6cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
(A) 288
(B) 48
(C) 36
(D) 864
(E) 964
Rationale: d=6, r=2;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*3*3*3= 36πcm3 ANSWER:C
Answer: (C) 36
Question: A river 2m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is?
(A) 4500 M3
(B) 4580 M3
(C) 7500 M3
(D) 4900 M3
(E) 4700 M3
Rationale: Explanation:
(5000 * 2 * 45)/60 = 7500 M3
Answer: Option C
Answer: (C) 7500 M3
Question: A train passes a train coming from opposite direction, speed 32 kmph in 25 sec. If the speed of the train is 40 km/hr. What is the length of train?
(A) 300
(B) 400
(C) 500
(D) 350
(E) 200
Rationale: Speed = (40+32) * 5/18 = 72 * 5/18 = 20 m/sec.
Length of the train = 25 * 20 = 500 m.
Answer: C
Answer: (C) 500
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 104 pounds?
(A) 8
(B) 7
(C) 16
(D) 10
(E) none of the above
Rationale: Ans is D:
39 pounds --> 6 days
104 pounds --> x days
x = 104*6/39 = 16
the animal has already consumed food in 6 days so the the number of days
for it's total consumption be 104 pounds is 16-6 = 10
Answer: (D) 10
Question: A motorcyclist goes from Nagpur to Pune, a distance of 500 kms at an average of 100 kmph speed. Another man starts from Nagpur by car 3 Â½ hours after the first, and reaches Pune Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:7
(C) 3:5
(D) 1:5
(E) 1:1
Rationale: T = 500/100 = 10 h
T = 10 - 4 = 6
Time Ratio = 10:6 = 5:3
Speed Ratio = 3:5
Answer: C
Answer: (C) 3:5
Question: A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 2:3
(C) 3:2
(D) 11:9
(E) 11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.
A : B
8000*18 : (8000*6) + (4000*12)
144000 : 96000
A:B = 3:2
ANSWER:C
Answer: (C) 3:2
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of grass ?
(A) Green
(B) BLUE
(C) PINK
(D) ORANCE
(E) BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of grass is 'Green' but in coding language, 'Green' is called 'Black'.
ANSWER: E
Answer: (E) BLACK
Question: If 4XZ + YW = 10 and XW + YZ = 20, what is the value of the expression (2X + Y)(2Z + W)?
(A) 9.
(B) 12.
(C) 15.
(D) 50.
(E) 18.
Rationale: (2x+y)*(2z+w) = 10+2(20) =50
Answer : D
Answer: (D) 50.
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.86. How much was lent at 5%?
(A) 228
(B) 299
(C) 400
(D) 500
(E) 188
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 â€“ 6x/100 = 86
x/100 = 4
=> x = 400
Answer:C
Answer: (C) 400
Question: A cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
(A) 28
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 4 x 1.25) + 4 x 4]
= 36
The answer is C.
Answer: (C) 36
Question: Hal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?
(A) 50
(B) 45
(C) 60
(D) 80
(E) 55
Rationale: Let's start with the concrete information:
He buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents).
He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items
Cost of each walnut = 1/5 = $.2 = 20 cents
Cost of each apple = 1/4 = $.25 = 25 cents
Now we have one equation to solve:
20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)
4w + 5(90 - w) = 390
w = 60
Answer (C)
Answer: (C) 60
Question: A cubical tank is filled with water to a level of 1 foot. If the water in the tank occupies 16 cubic feet, to what fraction of its capacity is the tank filled with water?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: The volume of water in the tank is H*L*B = 16 cubic feet.
Since H = 1, then L*B = 16 and L = B = 4.
Since the tank is cubical, the capacity of the tank is 4*4*4 = 64.
The ratio of the water in the tank to the capacity is 16/64 = 1/4
The answer is C.
Answer: (C) 1/4