mathewhe/aqua_rat huggingface dataset:
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 22
(B) 287
(C) 48
(D) 277
(E) 21
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer: C
Answer: (C) 48
Question: How many integers n are there such that 1< 5n +5 < 60?
(A) 5
(B) 7
(C) 11
(D) 13
(E) 12
Rationale: Solution:
1< 5n + 5 < 60 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know, to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.
1< 5n + 5 < 60
We first subtract 5 from all three parts of the inequality, and we obtain:
-4 < 5n < 55
Next, we divide both sides of the inequality by 5 and we get:
-4/5 < n < 11
The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 25.
The answer is C.
Answer: (C) 11
Question: A house wife saved $4 in buying an item on sale. If she spent $28 for the item, approximately how much percent she saved in the transaction?
(A) 8%
(B) 13%
(C) 10%
(D) 11%
(E) 12%
Rationale: Actual price = 28+4 = $32
Saving = 4/32 * 100 = 13% approximately
Answer is B
Answer: (B) 13%
Question: From 6 positive numbers and 6 negative numbers, how many groups F of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 625
(C) 30
(D) 960
(E) 255
Rationale: Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
F=15 +15 + 15*15 = 255=E
Answer: (E) 255
Question: If the first and second letters in the word DEPRESSION' were interchanged, also the third and the fourth letters, the fifth and the sixth letters and so on, which of the following would be the seventh letter from the right ?
(A) H
(B) K
(C) I
(D) P
(E) U
Rationale: Explanation:
The new letter sequence is EDRPSEISNO
The seventh letter from the right is P
Answer: D) P
Answer: (D) P
Question: One fourth of one third of two fifth of a number is 17. What will be 40% of that number
(A) 140
(B) 204
(C) 180
(D) 200
(E) 250
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 17 then x = 17 * 30 = 510
40% of 510 = 204
Answer: Option B
Answer: (B) 204
Question: If p and q are positive integers and q ≠ 1, then pq(q −5) is
(A) pq^2+5pq
(B) pq^2+pq
(C) pq^2-pq
(D) pq^2-5pq
(E) pq^2
Rationale: pq(q-5) = pq^2-5pq
Answer : D
Answer: (D) pq^2-5pq
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 1184
(B) 1151
(C) 1126
(D) 1130
(E) 1254
Rationale: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
ANSWER A
Answer: (A) 1184
Question: A car covers a distance of 840 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 187 kmph
(C) 164 kmph
(D) 140 kmph
(E) 106 kmph
Rationale: 840/6
= 140 kmph
Answer: D
Answer: (D) 140 kmph
Question: The diagonals of a rhombus are 14 cm and 20 cm. Find its area?
(A) 329
(B) 140
(C) 150
(D) 238
(E) 31
Rationale: 1/2 * 14 * 20 = 140
Answer: B
Answer: (B) 140
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.5
II. 15.3
III. 9.5
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
14.5 and 9.5 lies in the range of 2SD from mean
Answer: Option C
Answer: (C) II only
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/5 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
(A) 3/10
(B) 7/10
(C) 9/10
(D) 9/20
(E) 13/20
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (1/5)Y = (9/20)Y
The answer is D.
Answer: (D) 9/20
Question: A passenger sitting near the window in a train moving at 50 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 75 metres?
(A) a)50km/h
(B) b)52km/h
(C) c)56km/h
(D) d)60km/h
(E) e)40km/h
Rationale: im getting A
3 secs to pass a 75 mts train , therefore speed = 25 meters/sec
to convert m/s to km/hrs multiply by 3.6
25*3.6 = 90
so its 90-50 = 40 .
E
Answer: (E) e)40km/h
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
(A) 1/3
(B) 5/3
(C) 2/3
(D) 7/3
(E) 3/7
Rationale: . Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Option: A
Answer: (A) 1/3
Question: 4, 6, 9, 13.50, 20.25, (...)
(A) 60
(B) 60.75
(C) 58
(D) 31.528
(E) 30.375
Rationale: 4
(4Ã—3)Ã· 2 = 6
(6Ã—3)Ã· 2 = 9
(9Ã—3)Ã· 2 = 13.50
(13.50Ã—3)Ã· 2 = 20.25
(40.5Ã—3)Ã· 2 = 30.375
Answer is E
Answer: (E) 30.375
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 8786
(C) 8275
(D) 2872
(E) 2282
Rationale: A = 2000(21/20)2 = 2205
Answer:A
Answer: (A) 2205
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 140. The dividend from the stock is :
(A) 7.5 %
(B) 8.75 %
(C) 9.7 %
(D) None of these
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 140.
By investing Rs. 97, income = Rs. (140/1552x97)= Rs.8.75
âˆ´ Dividend = 8.75%.
Answer B
Answer: (B) 8.75 %
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 52 kmph
(B) 14 kmph
(C) 54 kmph
(D) 58 kmph
(E) 24 kmph
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Answer: C
Answer: (C) 54 kmph
Question: A train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 767 m
(B) 240 m
(C) 195 m
(D) 176 m
(E) 186 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 23 = 345 m.
Let the length of the platform be x m . Then,
(x + 345)/36 = 15 => x = 195 m.
Answer:C
Answer: (C) 195 m
Question: A jewelry store purchased a pair of earrings for $240 and was selling it at a price that equaled the purchase price of the earrings plus a markup that was 25 percent of the selling price. After some time a jewelry store owner decided to decrease the selling price by 20 percent. What was the jewelry store's gross profit on this sale?
(A) $14
(B) $2
(C) $10
(D) $16
(E) $18
Rationale: Sale Price(SP) = 240 + Markup(MP)
--> Mp = SP-240
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-240
3SP/4= 240
SP=320
Now a discount of 20% is given so NEW SP is .8 *320 =256
Profit=256-240 =16
Answer is D
Answer: (D) $16
Question: The difference between a 8 digit number and the number formed by reversing its digit is not a multiple of
(A) 3
(B) 5
(C) 296297
(D) 888891
(E) 2666673
Rationale: Another approach is to TEST a number.
Let's say the original number is 12000002
So, the REVERSED number is 20000021
The DIFFERENCE = 20000021-12000002 = 8000019
No check the answer choices
8000019 is a multiple of 3,296297,888891,2666673
5 is NOT a multiple of 8000019
Answer ; B
Answer: (B) 5
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years,9% p.a. for the next five years and 13% p.a. for the period beyond eight years.If the total interest paid by him at the end of eleven years is Rs. 8160,how much money did he borrow ?
(A) Rs. 8000
(B) Rs. 10,000
(C) Rs. 12,000
(D) Data inadequate
(E) None
Rationale: Solution
22.21
Let the sum be Rs. x.Then,
(X x6 x 3/100)+ (X x 9 x 5/100)+ (X x 13 x 3/100) 8160
18 x + 45x + 39x (8160x100)= 816000 x = 8000.
Answer A
Answer: (A) Rs. 8000
Question: How many multiples of 4 are there between 20 and 196 ?
(A) 45
(B) 42
(C) 52
(D) 43
(E) 51
Rationale: It should be mentioned whether 20 and 196 are inclusive.
If 20 and 196 are inclusive, then the answer is (196-20)/4+1=45.
If 20 and 196 are NOT inclusive, then the answer is (192-24)/4+1=43.
Since OA is D, then we have NOT inclusive case.
Answer: (D) 43
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/8
(B) 5/9
(C) 5/6
(D) 5/3
(E) 5/1
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵ ways.
The required probability = (5 * 4) = 20/36 = 5/9
Answer: B
Answer: (B) 5/9
Question: A coin is tossed 8 times. What is the probability of getting exactly 7 heads?
(A) 1/8
(B) 1/16
(C) 1/32
(D) 1/64
(E) 1/128
Rationale: The number of possible outcomes is 2^8 = 256
There are 8 ways to get exactly 7 heads.
P(exactly 7 heads) = 8/256 = 1/32
The answer is C.
Answer: (C) 1/32
Question: In an election between two candidates, 20% of votes are were declares invalid. First candidate got 480 votes which were 60% of the total valid votes . The total number of votes enrolled in that election was
(A) 2000 votes
(B) 3000 votes
(C) 3500 votes
(D) 3600 votes
(E) 3700 votes
Rationale: (100%-20%=80%
48%-32%=16%
16% = 16×30 = 480
100% =100×30 =3000 votes)
B
Answer: (B) 3000 votes
Question: After increasing 20% in the price of a Book costs Rs.240. Find the actual cost of an article?
(A) 100
(B) 150
(C) 200
(D) 220
(E) 250
Rationale: CP* (120/100) = 240
CP= 2* 100 => CP = 200
Answer:C
Answer: (C) 200
Question: The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8400 for a computer table, then what was the cost price of the computer table?
(A) Rs.6725
(B) Rs.6727
(C) Rs.6908
(D) Rs.6725
(E) Rs.7000
Rationale: CP = SP * (100/(100 + profit%))
= 8400(100/120) = Rs.7000.
Answer: E
Answer: (E) Rs.7000
Question: 6^5 is equal to which of the following?
(A) 7,776
(B) 8,752
(C) 9,660
(D) 2,662
(E) 1,608
Rationale: A is the correct answer. We do not really need to calculate it. The last digit for 6^5 will be 6. Hence A is the correct answer
Answer: (A) 7,776
Question: Set A contains all the even numbers between 42 and 90 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 300
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: Each term in set B is 20 more than the corresponding term in set A.
The difference of the sums = 25 * 20 = 500.
The answer is E.
Answer: (E) 500
Question: Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 80 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?
(A) 90
(B) 120
(C) 125
(D) 150
(E) 210
Rationale: let d=distance between cities A and B
bus 1 distance to first meeting=80 miles
bus 1 distance from first to second meeting=(d-80)+30=d-50 miles
bus 2 distance to first meeting=d-80 miles
bus 2 distance from first to second meeting=80+(d-30)=d+50 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 80/(d-50)=(d-80)/(d+50)
d^2=210d
d=210 miles
E
Answer: (E) 210
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270 m
(B) 870 m
(C) 290 m
(D) 278 m
(E) 275 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer:A
Answer: (A) 270 m
Question: How many of the factors of 1400 are divisible by 2?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: 1400 = 2^3*5^2*7
The total number of factors is (3+1)(2+1)(1+1) = 24
The odd factors are 1, 5, 7, 25, 35, and 175.
The number of even factors is 24-6 = 18
The answer is C.
Answer: (C) 18
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.85. What is the median gasoline price?
(A) $1
(B) $1.85
(C) $1.92
(D) $2.13
(E) $2.15
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.85, $1.96, $2.09, $2.11
The median gasoline price is $1.85. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.85
Question: Simplify: 7005-7000+10
(A) 6505
(B) 6305
(C) 6501
(D) 6508
(E) None of them
Rationale: 7005-7000+10
=7005-(7000/10)
=7005-700
=6305.
Answer is B
Answer: (B) 6305
Question: a bag of blue and green colored marbles has 50% green marbles, with a total of 40 marbles. how many green marbles need to be added to bring their percentage in the bag up to 80%?
(A) 60
(B) 58
(C) 42
(D) 24
(E) 80
Rationale: A bag of 40 marbles which is 50% green marbles means we have 20 green marbles. To get a bag that is 80% green marbles, let's use this expression: (20 + x)/(40 + x) = 0.8 with x representing the amount of green marbles that must be added to get to 80%. The expression thus represents the new number of green marbles over the total new number of marbles and this fraction should equal 80%. 60 marbles need to be added, as 80/100=0.8 or 80%
choose A
Answer: (A) 60
Question: A Bullock cart can travel at 10 kmph uphill road and downhill road 20 kmph. He takes 3 hours to row from lower point A to upper point B and back to A. What is the total distance traveled by bullock card in 3 hours? He must return back to base point A in remaining time.
(A) 80
(B) 20
(C) 30
(D) 40
(E) 60
Rationale: Upward distance traveled per hour - 10 km,
distance traveled after 2 hours = 20 km.
He remained with 1 hour travel downward, i.e. distance traveled in remaining 1 hour downward = 20 km
so total distance traveled from A to B and Back to point A = 20 km upward + 20 km downward = 40 km
(Answer : D)
Answer: (D) 40
Question: A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
(A) 180/18
(B) 180/15
(C) 180/13
(D) 180/12
(E) 180/11
Rationale: One day work of A and B = 1/12
One day work of B and C = 1/30
One day work of C and A = 1/36
2(A + B + C) = 1/12 + 1/30 + 1/36
2(A + B + C) = 13/90
(A + B + C) = 13/180
Number of days required = 180/13 days.
Answer: C
Answer: (C) 180/13
Question: A boy has 11 trousers and 11 shirts. In how many different ways can he select a trouser and a shirt?
(A) 121ways
(B) 130ways
(C) 90ways
(D) 100ways
(E) 139ways
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 11 * 11
= 121 ways.
Answer: A
Answer: (A) 121ways
Question: If 3<x<6<y<9, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3 < x < 6 < y < 9;
3 < x
y < 9
3 + y < x + 9
y - x < 6.
Positive integer difference is 5 (for example y = 8.5 and x = 3.5)
Answer: C.
Answer: (C) 5
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 302 to 398, inclusive?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 302 x 304 x 306 x 308 => unit digit 4
312 x 314 x 316 x 318 => unit digit 4
392 x 394 x 396 x 398 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer: C
Answer: (C) 6
Question: The simple interest on a sum of money will be Rs.1200 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 8981
(B) 3799
(C) 1200
(D) 2400
(E) 1732
Rationale: P --- 10 ---- 1200
P --- 5 ----- 600
3P --- 5 ----- 1800
------
=> 2400
Answer: D
Answer: (D) 2400
Question: 4, 12, 48, 240, 1440, (...)
(A) 7620
(B) 10080
(C) 6200
(D) 10020
(E) 12500
Rationale: Explanation :
Go on multiplying the given numbers by 3, 4, 5, 6, 7
Answer : Option B
Answer: (B) 10080
Question: A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 50 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
(A) 500.
(B) 412.
(C) 432.
(D) 502.
(E) 522.
Rationale: Pastry is divided in 50 customers equally. So,total number of pastry must be a multiple of 50
Only option A satisfies the condition, and hence is the answer
Answer: (A) 500.
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [5]*[6] equivalent to?
(A) [45]
(B) [30]
(C) [15]
(D) [5]
(E) [50]
Rationale: [5]*[6] = 15*3 = 45 = [15]
The answer is C.
Answer: (C) [15]
Question: Eight men, ten women and six boys together can complete a piece of work in eight days. In how many days can 20 women complete the same work if 20 men can complete it in 12 days?
(A) 33m
(B) 77m
(C) 66m
(D) 22m
(E) 88m
Rationale: Let the number of units which can be completed by each man, each women and each boy be m/day, w/day and b/day respectively.
Work = 8(8m + 10w +6b)units = 12(20m)
10w +6b = 22m
b is unknown.
We cannot find the relation between m and w.
We cannot answer the question.
Answer: D
Answer: (D) 22m
Question: In 2005, 25 percent of the math department’s 40 students were female, and in 2007, 40 percent of the math department’s 85 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
(A) 15%
(B) 50%
(C) 62.5%
(D) 115%
(E) 240%
Rationale: Female students in 2005 = 25% of 40 = 10
Female students in 2007 = 40% of 85 = 34
Percentage increase = [(34- 10)/10] *100 % = 240%
Correct Option: E
Answer: (E) 240%
Question: In a village there are 4 programs organised for the festival. The festival occurs for 2 days. In how many ways that the 2 programs can be divided for 2 days?
(A) 4
(B) 10
(C) 6
(D) 5
(E) 2
Rationale: There are 4 programs for 2 days festival. That is Each day has 2 Programs.
The question is how many ways that the programs is chosen.
4C2=4!/2!*2!=4*3*2!/2!*2*1
4C2=6
There are 6 possible ways to organise the programs
Answer: (C) 6
Question: Pipes A and B fill a tank in 5 and 6 hours respectively. Pipe C empties the tank in 12 hours, if you open all the three pipes together this tank will be filled in?
(A) 3 9/17 hours
(B) 4.5 hours
(C) 1.25 hours
(D) 4 7/17 hours
(E) None of these
Rationale: Explanation:
It is given that Pipe A,B and C work simultaneously.
Pipe A and B are filling the tank and Pipe C is emptying it.
In 1 hour volume of tank filled by Pipe A: 1/5th
In 1 hour volume of tank filled by Pipe B: 1/6th
In 1 hour volume of tank emptied by Pipe C: 1/12th
Working together Pipe A B and C fill x volume of tank.
=>1/x = (1/5)+(1/6)-(1/12)
=>x=60/17 hours
ANSWER A
Answer: (A) 3 9/17 hours
Question: In a class of 50 students the number of females is 2 more that 5 times the male number .How many males and females are there in the class
(A) 42, 8
(B) 50,8
(C) 8,42
(D) 8,50
(E) 40,10
Rationale: Let the females be x and males be y
x+y=50--1
x=5y+2---2 This can be written as x-5y=2---3
solving 1 and 3 we get y=8
substituting y=8 in (1) we get x=42
Correct ans is A
Answer: (A) 42, 8
Question: Jim wishes to buy 3 gifts that cost 15 dollars, 9 dollars, and 8 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
(A) $57
(B) $47
(C) $7
(D) $17
(E) $24
Rationale: $15 + $9 + $8 = $32 needed
1/4 x $32 = $8 on hand
$32 - $8 = $24 to earn
correct answer E
Answer: (E) $24
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 22 kmph
(B) 77 kmph
(C) 54 kmph
(D) 71 kmph
(E) 88 kmph
Rationale: S = 240/16 * 18/5 = 54 kmph
Answer:C
Answer: (C) 54 kmph
Question: What percent is 25 gm of 1 kg?
(A) 0.5 %
(B) 1%
(C) 1.5%
(D) 2.5%
(E) 3%
Rationale: 1 kg = 1000 gm
25/1000 × 100 = 2500/1000
=5/2 = 2.5 %
D)
Answer: (D) 2.5%
Question: The price of a T.V. set worth Rs. 30000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 22678
(B) 26699
(C) 29000
(D) 19000
(E) 26711
Rationale: Money paid in cash = Rs. 1000
Balance payment = (30000 - 1000) = Rs. 29000
Answer: C
Answer: (C) 29000
Question: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 12 cm?
(A) 243cm2
(B) 239cm2
(C) 267cm2
(D) 230cm2
(E) 228cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (12)
= 228 cm2
Answer:E
Answer: (E) 228cm2
Question: Yesterday, a pie shop sold 6 apple pies, 5 peach pies, and 6 pumpkin pies. How many pies did the shop sell in all?
(A) 21
(B) 37
(C) 13
(D) 17
(E) 32
Rationale: Add the number of pies
6+5+6 =17.
Answer is D.
Answer: (D) 17
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
(A) 1/26
(B) 1/27
(C) 1/29
(D) 1/37
(E) 1/97
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13
= 1/26
Answer: A
Answer: (A) 1/26
Question: A and B starts a business with Rs.8000 each, and after 3 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 22:13
(C) 23:12
(D) 12:7
(E) 11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 3 months and then withdraws Rs.4000. So, the investment of B for remaining 15 months is Rs.4000 only.
A : B
8000*18 : (8000*3) + (4000*15)
144000 : 84000
A:B = 12:7
ANSWER:D
Answer: (D) 12:7
Question: The ratio of number of boys and girls in a school is 2:5. If there are 210 students in the school, find the number of girls in the school?
(A) 150
(B) 250
(C) 300
(D) 370
(E) 280
Rationale: Let the number of boys and girls be 2x and 5x
Total students = 210
Number of girls in the school = 5*210/7 = 150
Answer is A
Answer: (A) 150
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for t dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
(A) x/(y - t)
(B) x/(t - y)
(C) x
(D) x/t
(E) x/y
Rationale: Two ways...
1) let a be the total number, so cost = a*y+x and selling price=a*t..
No profit no loss....a*y+x=a*t.....a=x/(t-y)...
B
Answer: (B) x/(t - y)