mathewhe/aqua_rat huggingface dataset:
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
(A) 12 kg
(B) 60 kg
(C) 72 kg
(D) 96 kg
(E) None of these
Rationale: Explanation:
Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.06 x 1000)kg
= 60 kg.
Answer: B
Answer: (B) 60 kg
Question: if p/q=3/4
then3p+8q=?
(A) 25/4
(B) 25/2
(C) 20/4
(D) 41/4
(E) 25/3
Rationale: 3p+8q=?
Divided by q,
3(p/q)+8=x
3*(3/4)+8=41/4
ANSWER:D
Answer: (D) 41/4
Question: A man took loan from a bank at the rate of 10% p.a. simple interest. After 3 years he had to pay Rs. 3000 interest only for the period. The principal amount borrowed by him was:
(A) 8000
(B) 10000
(C) 11000
(D) 12000
(E) 13000
Rationale: Principal = (100X3000)/(10X3)= Rs. 10000
answer : B
Answer: (B) 10000
Question: The ratio between the speeds of two trains is 8: 9. If the second train runs 270 kms in 3 hours, then the speed of the first train is ?
(A) 85 km/hr
(B) 835 km/hr
(C) 80 km/hr
(D) 82 km/hr
(E) None of these
Rationale: Explanation:
Let the speeds of two trains be 8X and 9X km/hr.
9/X=270/3=>X=10Km/hr
So speed of first train is 10*8 = 80 km/hr
Option C
Answer: (C) 80 km/hr
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2 or3?
(A) 1/2
(B) 1
(C) 1/6
(D) 4/6
(E) 5/6
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
Let F be the event of getting the multiple of 2
then ,E={2,4,6}
Let G be the event of getting the multiple of 2 and 3
then ,G={2,3,4,6}
P(G)=n(G)/n(S)=4/6
ans D
Answer: (D) 4/6
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 174 votes. Find the total number of valid votes?
(A) 435
(B) 570
(C) 480
(D) 520
(E) 550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 174 => 4x/10 = 174
=> 4x = 1740 => x = 435.
ANSWER:A
Answer: (A) 435
Question: Mrs. A. invested $21,000; part at 5%, and part at 8%. The total interest on the investment was $1,470. How much did she invest at each rate?
(A) x=$15,000, y =$30,000
(B) x=$12,000, y =$24,000
(C) x=$8,000, y =$16,000
(D) x=$10,000, y =$20,000
(E) x=$7,000, y =$14,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $1,470 is 7% of 21,000
In which answer choice is y = 2(x)
Answer E
Answer: (E) x=$7,000, y =$14,000
Question: In a class, 30 students pass in English and 20 students in Math, while some students among these pass in both. How many more students do only English as compared to those doing only Maths?
(A) 10
(B) 15
(C) 20
(D) 25
(E) Indeterminate
Rationale: Let us consider tht x student are tohse who passed in both English and Maths...
So first we remove x student from both of them
Therefore,
English = 30-x
Maths = 20-x
Now, Number of Students more in English = (30-x)-(20-x)
= 30-x-20+x
= 10
ANSWER:A
Answer: (A) 10
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
(A) 230 m
(B) 270m
(C) 643m
(D) 832m
(E) 270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 250/26	= 20
x + 250 = 520
x = 270.
Answer:B
Answer: (B) 270m
Question: The errand service company gets a discount at the fuel center when they fill up more than 4 cars at a time. The service is $1.10 per vehicle and .30 cents per liter of fuel. On Monday , they will fill 3 vans and 3 cars. The cars are 25 liters each and the vans are 60% bigger. How much will it cost to fill up all vehicles if they are empty?
(A) $65.50
(B) $68.10
(C) $67.50
(D) $68.50
(E) $65.10
Rationale: Lots of calculations.
1.10*6 + 3*25*.30+ 25*(8/5)*3*.30
Answer=$65.10
The correct option is E.
Answer: (E) $65.10
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
(A) Friday
(B) Saturday
(C) Sunday
(D) Wednesday
(E) WednSDA
Rationale: n 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answer: A
Answer: (A) Friday
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 12:15:17
(B) 12:15:16
(C) 12:15:10
(D) 12:15:155
(E) 12:15:11
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Answer: (B) 12:15:16
Question: Complete the series 95, 115.5, 138, ..., 189
(A) 189
(B) 198
(C) 178
(D) 187
(E) 193
Rationale: 95 + 20.5 = 115.5
115.5 + 22.5 = 138
138 + 24.5 = 162.5
162.5 + 26.5 = 189
Answer is A.
Answer: (A) 189
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.3 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
(A) $1.75
(B) $1.85
(C) $2.00
(D) $2.12
(E) $2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 30 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $8.25 (a 30-cent increment) and the the difference in sequential prices of the pots is 30 cents, the largest pot PROBABLY has a price that is a 30-cent increment. From the answer choices, I would then TEST Answer D
IF....
The largest pot = $2.125
The other 5 pots are....
0.625
0.925
1.225
1.525
1.825
2.125
Total = $8.25
So this MUST be the answer.
D
Answer: (D) $2.12
Question: Evaluate the sum
1-2 +3-4 + 5-6 +... + 997-998 + 999-1000
(A) -500
(B) -1000
(C) -999
(D) -1001
(E) 500500
Rationale: One groups the first two terms and each successive two terms to obtain a sum of
500 expressions each of which is -1. The answer is -500
correct answer A
Answer: (A) -500
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 Â½ sec
(B) 6 Â½ sec
(C) 9 Â½ sec
(D) 9 sec
(E) 7 Â½ sec
Rationale: D
9 sec
D = 180
S = 72 * 5/18 = 20 mps
T = 180/20 = 9 sec
Answer: (D) 9 sec
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, 17, 22, 20, (....)
(A) 27
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22, 27) increasing by 3 and 5 respectively.
answer : A
Answer: (A) 27
Question: A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
(A) 50 kmph
(B) 70 kmph
(C) 60 kmph
(D) 80 kmph
(E) 10 kmph
Rationale: Explanation:
Speed on return trip = 150% of 50 = 75 km/hr.
Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.
Answer: C
Answer: (C) 60 kmph
Question: A pair of articles was bought for $1000 at a discount of 10%. What must be the marked price of each of the article?
(A) $555.55
(B) $500
(C) $350
(D) $400
(E) $600
Rationale: S.P. of each of the article = 1000/2 = $500
Let M.P = $x
90% of x = 500
x = 500*100/90 =$555.55
Answer is A
Answer: (A) $555.55
Question: In a hotel we can order two types of varities,but we can make 6 more variteis in home.One can choosethe four varities with two from hotel as must.Find how many ways one can order.
(A) 14
(B) 15
(C) 56
(D) 28
(E) 30
Rationale: No. of ways=2c2*6c2=15
ANSWER:B
Answer: (B) 15
Question: If 2/z = 2/(z + 1) + 2/(z + 25) which of these integers could be the value of z?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:
A. 2/0 = 2/1 +2/25 INCORRECT (Division by zero)
B. 2/1 = 2/2 +2/26 INCORRECT
C. 2/2 = 2/3 +2/27 INCORRECT
D. 2/3 = 2/4 +2/28 INCORRECT
E. 2/4 = 2/5 +2/30 CORRECT
The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: (E) 5
Question: A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days?
(A) 12
(B) 15
(C) 8
(D) 10
(E) 11
Rationale: (A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12
(1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5
(A+B+C) work in 1 day= 1/10
So,all three together finish work in 10 days
Answer D
Answer: (D) 10
Question: If x is 40 percent greater than 88, then x =
(A) 68
(B) 70.4
(C) 123.2
(D) 105.6
(E) 108
Rationale: x=88*1.4=123.2
So the answer is C.
Answer: (C) 123.2
Question: Of the mutual funds on a “select list,” 2/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 100 funds on the list have 3-star ratings, how many funds are on the list?
(A) 500
(B) 750
(C) 1,000
(D) 1,200
(E) 1,500
Rationale: A
Fraction of 5- and 4-star funds: 2/3 + (2/5)*(1/3) = 2/3 + 2/15 = 12/15=4/5
Fraction of 3-star funds = 1 - 4/5 = 1/5
(1/5)*Total = 100
Total = 500
Answer: (A) 500
Question: How many positive integers will divide evenly into 440?
(A) 8
(B) 12
(C) 16
(D) 18
(E) 20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18
Option D
Answer: (D) 18
Question: The bankerâ€™s discount of a certain sum of money is Rs. 80 and the true discount on the same sum for the same time is Rs. 70. The sum due is
(A) 210
(B) 280
(C) 560
(D) 450
(E) None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[80 * 70 / 80 - 70] = Rs. [80 * 70 / 10] = Rs. 560
Answer C
Answer: (C) 560
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $50 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
(A) $5
(B) $10
(C) $14
(D) $24
(E) $28
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $50
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 50
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 50
i.e. x = 26
i.e. Fixed Monthly Charge, y = 26
Answer: D
Answer: (D) $24
Question: The average of 45 students in a class is 18 years. The average age of 21 students is 16. What is the average age of remaining 14 students?
(A) 21
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Sum of the ages of 14 students
= (18* 45) - (18 * 21) = 810 - 378 = 432
Required average = (266/23)
= 18 years.
Answer: D
Answer: (D) 18
Question: If 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x
(A) 72
(B) 58
(C) 64
(D) 29
(E) 28
Rationale: Explanation:
The given equations are :
2x + 3y = 30 --------- (i)
and, (x+y)/y = 11/8
8x + 8y = 11y
8x – 3y =0 ----(ii)
Adding (i) & (ii), we get : 10 x = 30 or x = 3.
Put x = 3 in (i), we get : y = 8
Therefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.
ANSWER: B
Answer: (B) 58
Question: If 0 < c < 1, what is the median of the values c, c^-1, c^2, c^1/2 and c^3?
(A) c
(B) c^-1
(C) c^2
(D) c^1/2
(E) c^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as c = 1/4 and calculate:
c = 1/4
c^-1 = 4
c^2 = 1/16
c^(1/2) = 1/2
c^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is c. Answer A
Answer: (A) c
Question: A tank is filled by 3 pipes A,B,C in 4 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
(A) 25hr
(B) 35hr
(C) 40hr
(D) 20hr
(E) 28hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/4
7/x = 1/4
x = 28 hours
Answer is E
Answer: (E) 28hr
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 300meters, after what time will they meet at the starting point?
(A) 20sec
(B) 15sec
(C) 30sec
(D) 50sec
(E) 1min
Rationale: They meet every 300/7+8 = 20sec
Answer is A
Answer: (A) 20sec
Question: A company’s eight trucks running 3 hrs a day can carry 1,200 packs of produce. The company invested in 4 new trucks and got rid of 2 of the previous ones. The new trucks can carry 0.5% more produce than the old ones. How many produce in total can be delivered within the next 2 days for 4 hours?
(A) 4,800
(B) 9,200
(C) 4,400
(D) 3,600
(E) 800
Rationale: Old trucks can carry (1,200/8)/3 = 50 per hour each.
New trucks carry 1.5*50= 75 per hour each.
In total, 6 old trucks + 2 new trucks is (6*75*4 hours*2 days) + (2*50*4 hours*2 days)= 4,400.
Answer is option C.
Answer: (C) 4,400
Question: Today is Monday. After 30 days, it will be :
(A) Thursday
(B) Saturday
(C) Monday
(D) Sunday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 28 days, it will be Monday.
After 30 days, it will be Wednesday.
Answer is E
Answer: (E) Wednesday
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 15 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 15 more blue balls than white balls...
Equation #2: y = 15 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 15
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 15) = 100
5y - 15 = 100
5y = 115
y = 23
There are 23 blue balls. This is 15 more than the number of white balls, so z = 8. That's the answer. Just as a check, x = 69, and 69 + 23 + 8 = 100.
Answer = 8,(A)
Answer: (A) 8
Question: There are 20 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
(A) 20
(B) 25
(C) 30
(D) 45
(E) 60
Rationale: Note that each handshake includes two people.
The total number of handshakes is 20*3/2 = 30
The answer is C.
Answer: (C) 30
Question: The food in a camp lasts for 25 men for 40 days. If fifteen more men join, how many days will the food last?
(A) 25 days
(B) 30 days
(C) 20 days
(D) 16 days
(E) 27 days
Rationale: one man can consume the same food in 25*40 = 1000 days.
15 more men join, the total number of men = 40
The number of days the food will last = 1000/40 = 30 days.
Answer:A
Answer: (A) 25 days
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench?
(A) 720
(B) 730
(C) 740
(D) 750
(E) 800
Rationale: npn = n!
6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720
A
Answer: (A) 720
Question: What is the sum of the integers from -60 to 65, inclusive?
(A) 315
(B) 215
(C) 115
(D) 165
(E) 765
Rationale: In an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=65, a=-60, d=1
hence, 65=-60+(n-1)
or n=126
Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms
sn=126*(-60+65)/2
sn=126*5/2 = 315
Answer : A
Answer: (A) 315
Question: The new swimming pool needs to be filled with water. If the swimming pool is 5m^3, and the speed to fill the swimming pool is 2.5 cm^3/sec (1m^3 = 10^6 cm^3), how long does it take to fill the entire swimming pool?
(A) 2*10^3
(B) 2*10^4
(C) 2*10^5
(D) 2*10^6
(E) 2*10^7
Rationale: From 1 m^3 = 10^6 cm^3, 5m^3 = 5*10^6 cm^3, time = 5*10^6 cm^3 / 2.5cm ^3/sec = 2*10^6 seconds. Correct Option: 2*10^6 Answer: D
Answer: (D) 2*10^6
Question: A certain bag contains 60 balls — 22 white, 18 green, 17 yellow, 3 red, and 1 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.09
(B) 0.15
(C) 0.54
(D) 0.85
(E) 0.95
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 17)/60 = 57/60 = 0.95.
Answer: E.
Answer: (E) 0.95
Question: John invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 2 years and to $ 500 at the end of another 3 years. What was the rate of interest in which he invested his sum?
(A) 12%
(B) 40%
(C) 6.67%
(D) 25%
(E) 33%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 2years the principal P amounts to $300 and after a time of 5years ( question says after another 3years so 2+3) P becomes $500.
Formulating the above data
Amount (A1) at end of 2years
A1= P(1 + 2R/100) = 300
Amount (A2) at end of 8years
A2 = P(1 + 5R/100) = 500
Dividing A2 by A1 we get
(1 + 5R/100)/(1 + 2R/100) = 5/3
after cross multiplication we are left with 5R =100*2 which gives R = 40%
Option: B
Answer: (B) 40%
Question: 100 men started working to complete a work in 50 days.After working 8hours/day they had completed 1/3rd of the work in 25 days.How many men should be hired so that they will finish the work in time by working 10 hours/day.
(A) 30 men
(B) 60 men
(C) 90 men
(D) 100 men
(E) 120 men
Rationale: Working 8 hours/day, in 25 days, 100 men completes 8*25*100= 20000 men hours which is 1/3 of the work, So remaining 2/3 work to be completed =20000*(2/3)/(1/3)=40000 men hours.
If with 'x' extra men hired ,remaining work is to be completed in 50-25=25 days , working 10 hours/day, then, (100+x)*25*10=40000, 25000+250x=40000, x=60 men
ANSWER:B
Answer: (B) 60 men
Question: What is the total number of integers between 10 and 100 (exclusive)that are divisible by 7?
(A) 10
(B) 13
(C) 15
(D) 12
(E) 11
Rationale: 14, 21, 28, ..., 91,98
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (98 - 14) / (7) + 1 = 12 + 1 = 13
Answer is B
Answer: (B) 13
Question: When a 192 meters long rod is cut down into small pieces of length 3.0 meters each. Then how many pieces are available ?
(A) 52
(B) 68
(C) 62
(D) 64
(E) 69
Rationale: Answer
No. of pieces = Total length / Length of each piece
= 192/3.0
= 64
Option: D
Answer: (D) 64
Question: If T = 5/9 * (K - 32), and if T = 75, then what is the value of K?
(A) 158
(B) 161
(C) 164
(D) 167
(E) 170
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(75)/5 + 32 = 167
The answer is D.
Answer: (D) 167
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
(A) 12.8
(B) 12.4
(C) 12.5
(D) 16.8
(E) 92.7
Rationale: 1000*15
= 1200*x
x = 12.5
Answer: C
Answer: (C) 12.5
Question: 320 students are to embark on an excursion. What is the smallest possible number of vans that are needed to transport all 320 students, if a van can carry 18 students only?
(A) 18
(B) 17
(C) 14
(D) 12
(E) 13
Rationale: To find the number of vans, we divide 320 by 22.
320/18 = 17 and remainder = 14
So 17 vans are needed to transport 320 students, and 1 van is needed to transport the 14 remaining students . A total of 18 vans are needed.
correct answer A
Answer: (A) 18
Question: Income and expenditure of a person are in the ratio 7 : 6. If the income of the person is Rs. 14000, then find his savings?
(A) 500
(B) 1000
(C) 1500
(D) 2000
(E) 2500
Rationale: Let the income and the expenditure of the person be Rs. 7x and Rs. 6x respectively.
Income, 7x = 14000
=> x = 2000
Savings = Income - expenditure
= 7x - 6x = x
So, savings =Rs.2000.
Answer: D
Answer: (D) 2000
Question: The price of precious stone is directly proportional to square of its weight. what will be the loss incurred if a stone weighing 28gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15:13?
(A) No loss
(B) 10,000
(C) 28,000
(D) 9,500
(E) 14,000
Rationale: x=28000/28^2=35.71
cost of 15g=35.71*15^2=8035.714
cost of 13g=35.71*13^2=6035.714
total cost=14071.428
loss=28000-14071.428=13928.5=14000
ANSWER:E
Answer: (E) 14,000
Question: How many times in a day, the hands of a clock are straight?
(A) 22
(B) 34
(C) 44
(D) 54
(E) 76
Rationale: In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer:C
Answer: (C) 44
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?
(A) 130 m
(B) 140 m
(C) 150 m
(D) 170 m
(E) 190 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: (C) 150 m
Question: Which of the following is the sum of all the even numbers between 1 and 95, inclusive?
(A) 2550
(B) 2448
(C) 2600
(D) 2499
(E) 2652
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 95, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
6+94 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-2 = 2448
Final Answer:
B
Answer: (B) 2448
Question: In State X, all vehicle license plates have 1 letter from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
(A) 23,400
(B) 60,840
(C) 67,600
(D) 608,400
(E) 260,000
Rationale: The choices give us the answer without any calculations--
4 one digits places can take 10*10*10*10 ways..
1 letter places can be filled up in 26 ways
ans= 26*10*10*10*10=260000
ans E
Answer: (E) 260,000
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
(A) 13 minutes
(B) 14 minutes
(C) 15 minutes
(D) 16 minutes
(E) 17 minutes
Rationale: Solution:
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Answer C
Answer: (C) 15 minutes