mathewhe/aqua_rat huggingface dataset:
Question: Shweta buys a product at 25% discount rate. At what % over the cost price should she sell the product to make an overall 25% profit over the listed price?
(A) 25
(B) 33.333
(C) 66.667
(D) 40
(E) None of these
Rationale: Explanation:
Let listed price of the product be x
Hence at 25% discount rate the Cost Price will become: 3x/4
Now to make an overall profit of 25% over listed price:
SP = CP+(25/100)CP
=> SP = x+x/4
=>SP = 5x/4
=>Selling Price over Cost price: (5x/4)-(3x/4)
=>x/2
=>%Selling price over Cost price: (x/2)/(3x/4)*100
=>66.67%
ANSWER C
Answer: (C) 66.667
Question: When n is divided by 24, the remainder is 3. Find thee difference between previous remainder and the remainder when 9n is divided by 7 ?
(A) 2
(B) 7
(C) 5
(D) 3
(E) 6
Rationale: Let n=3 (leaves a remainder of 3 when divided by 24)
9n = 9(3) =27, which leaves a remainder of 6 when divided by 7.
difference = 6 - 3 = 3.
Answer D
Answer: (D) 3
Question: Peter age after 5 years will be 5 times his age 5 years back. what is the present age of Peter?
(A) A)20
(B) B)25
(C) C)15
(D) D)22
(E) E)10
Rationale: Peter present age= x
after 5 years = x+5
5 years back = x-5
x+5= 5(x-5)
x=20
Answer is A
Answer: (A) A)20
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) Rs.2.8
(B) Rs.2.4
(C) Rs.2.5
(D) Rs.2.2
(E) Rs.2.1
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer:C
Answer: (C) Rs.2.5
Question: What will be the output of the following code statements?
Integer a = 15, b = 30, c = 10 print (a × b / c) – c
(A) 35
(B) 26
(C) 29
(D) 26
(E) 81
Rationale: Explanation:
Apply BODMAS rule
15 × 30 = 450/10-10 =45 –10 =35
Answer:A
Answer: (A) 35
Question: A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 126 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?
(A) 2
(B) 4
(C) 1
(D) 5
(E) 3
Rationale: We have to work with multiples of 20 and 25.
First, we must know the limits of this multiples, so:
126/25= 5....so the max is 5
126/20=6...so the max is 6
126-125 =1 (5 big box or 5 small box +1 big box)
Answer : C
Answer: (C) 1
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was bom. If my sister was 4 years of age when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
(A) 32 yrs, 23 yrs
(B) 32 yrs, 29 yrs
(C) 35 yrs, 29 yrs
(D) 35 yrs, 33 yrs
(E) None
Rationale: Solution
Clearly,my mother was born 3 years before I was born and 4 years after my sister was born.
So, father's age when brother was born	=(28+4)
= 32 years.
mother's age when brother was born	=(26 - 3)
= 23 years.
Answer A
Answer: (A) 32 yrs, 23 yrs
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 7 can be used only once?
(A) 20
(B) 150
(C) 304
(D) 310
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Numbers with seven 7-s,7X7X 4*1*1*4=16.
Thus there are 320-16=304 such numbers.
Answer: C.
Answer: (C) 304
Question: Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 3 minutes, then how much more time will it take to fill the tank by tap B?
(A) 6 min 45 sec
(B) 5 min 45 sec
(C) 2min 45 sec
(D) 5 min 55 sec
(E) 5 min 28 sec
Rationale: Part filled by pipe A in 1 minute = 18
Part filled by pipe B in 1 minute = 1/14
Part filled by pipe A and pipe B in 1 minute = 1/8+1/14=11/56
Pipe A and pipe B were open for 3 minutes
Part filled by pipe A and pipe B in 3 minutes = (3×11)/56=33/56
Remaining part = 1−(33/56)=23/56
Time taken by pipe B to fill this remaining part =(23×14)/56=23/4 minutes= 5 minutes 45 seconds
Answer is B
Answer: (B) 5 min 45 sec
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams G could be selected from the eight candidates?
(A) 56
(B) 120
(C) 210
(D) 1120
(E) 6720
Rationale: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways G= 8*7*20=1120..
ans D...
Answer: (D) 1120
Question: The probability that a visitor at the mall buys a pack of candy is 50%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
(A) 0.225
(B) 0.25
(C) 0.325
(D) 0.375
(E) 0.5
Rationale: One case is: candy - candy - no candy
The probability is 5/10*5/10*5/10 = 125/1000
There are 3 such cases, so we should multiply this probability by 3.
P(exactly 2 buy candy) = 125/1000 * 3 = 375/1000 = 0.375
The answer is D.
Answer: (D) 0.375
Question: A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.8 that the job will be completed on time if there is no strike, 0.32 that the job will be completed on time. If there is a strike. Determine the probability that the job will be completed on time.
(A) 0.488
(B) 0.485
(C) 0.486
(D) 0.458
(E) 0.487
Rationale: Assume A = There will be a strike
B = Construction Job will be completed on time
P(A) = 0.65 and P(A1)P(A1) = 1 - 0.65 = 0.35
P(B|A) = 0.32 and P(B|A1)=0.8
P(B)=P(A).P(B|A)+P(A1).P(B|A1)
= 0.65×0.32+0.35×0.8=0.488
Answer A
Answer: (A) 0.488
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number W of employees who take the subway to work?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible W: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: (D) 15
Question: In a garments industry, a loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
(A) 194 sec
(B) 195 sec
(C) 196 sec
(D) 200 sec
(E) None of these
Rationale: Explanation :
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 25 : x
=> x = 25 * 1/0.128
=> x = 195.31
So time will be approx 195 seconds
Answer : B
Answer: (B) 195 sec
Question: A student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly ?
(A) 12
(B) 16
(C) 18
(D) 24
(E) 26
Rationale: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 48 3x = 48 x = 16.
Answer:B
Answer: (B) 16
Question: If a:b=2:8 and b:c=3:4 find a:b:c?
(A) 3:12:16
(B) 12:3:6
(C) 6:12:3
(D) 4:3:14
(E) 5:2:6
Rationale: a:b = 2:8, b:c = 3:4
2:8
3:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:12:16
A
Answer: (A) 3:12:16
Question: How many times will the digit 4 be written when listing the integers from 1 to 1000?
(A) 512
(B) 300
(C) 294
(D) 264
(E) 385
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 4) 3000/10=300 times.
Answer: B.
Answer: (B) 300
Question: Find the odd man out
385, 462, 572, 427, 671, 264
(A) 385
(B) 427
(C) 671
(D) 264
(E) 462
Rationale: add 1st and 3rd term nd get mid term
3+5 = 8
4+2 = 6
5+2 = 7
4+7 = 11
6+1 = 7
2+4 = 6
ANSWER:B
Answer: (B) 427
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 276
(B) 30
(C) 88
(D) 266
(E) 12
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
Answer:B
Answer: (B) 30
Question: If x - y =1 and
x2+y2=25
, find the value of ab.
(A) 8
(B) 12
(C) 16
(D) 32
(E) 48
Rationale: Explanation:
We know
2ab=(a2+b2)âˆ’(aâˆ’b)2
2xy=25âˆ’1=24
=>xy=12
OptionB
Answer: (B) 12
Question: A broker invested her own money in the stock market. During the first year, she increased her stock market wealth by 80 percent. In the second year, largely as a result of a slump in the stock market, she suffered a 30 percent decrease in the value of her stock investments. What was the net increase or decrease on her overall stock investment wealth by the end of the second year?
(A) −5%
(B) 5%
(C) 15%
(D) 26%
(E) 80%
Rationale: The actual answer is obtained by multiplying 180% by 70% and subtracting 100% from this total. That is: 180% × 70% = 126%; 126% − 100% = 26%.
Answer: D
Answer: (D) 26%
Question: There are cats got together and decided to kill the mice of 999936. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
(A) 941,1009
(B) 991,1001
(C) 991,1009
(D) 992,1008
(E) 931,1009
Rationale: 999936 can be written as 1000000 â€“ 64
= 10002 â€“ 82 ie of the form a2-b2=(a+b)(a-b)
=(1000+8)*(1000-8)
= (1008)*(992)
Given that number of cats is less than number if mice.
So number of cats is 992 and number of mice were 1008
Answer D
Answer: (D) 992,1008
Question: The distance between X&Y is 600km. A person is traveling from X to Y at 60km/hr started at 10AM and another person is traveling from Y to X at 40km/hr and started at same time. Then at what time they meet together.?
(A) A)2PM
(B) B)4PM
(C) C)1PM
(D) D)3PM
(E) E)5PM
Rationale: Let x hours be they will meet together
distance covered by 1st person+distance covered by 2nd person = 600km
60x+40x = 600
x= 6 hr
They will meet = 10AM +6hr = 4PM
Answer is B
Answer: (B) B)4PM
Question: Double of Quarter of 3 percent written as a decimal is :
(A) 0.003
(B) 0.015
(C) 0.25
(D) 0.005
(E) None of these
Rationale: Explanation :
Solution: (2)*(1/4)*3% = 2*(1/4 * 3/100) = 0.015.
Answer : B
Answer: (B) 0.015
Question: A person travels from P to Q a speed of 60 km/hr and returns by increasing his speed by 20%. What is his average speed for both the trips?
(A) 33
(B) 77
(C) 48
(D) 66
(E) 21
Rationale: Speed on return trip = 120% of 60 = 72 km/hr.
Average speed of trip = 60 + 72 /2 = 132/2 = 66 km/hr
Answer : D
Answer: (D) 66
Question: The least number which should be added to 3725 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
(A) 45
(B) 55
(C) 65
(D) 75
(E) 85
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 3725 by 60, the remainder is 5.
Number to be added = (60 - 5) = 55
B)
Answer: (B) 55
Question: A train 360 m long is running at a speed of 45 km / hr. In what time will be pass a bridge 140 m long?
(A) 40 sec
(B) 42 sec
(C) 45 sec
(D) 48 sec
(E) None
Rationale: Sol.
Speed = [45x5/18] m/sec = 25/2 m/sec.
Total distance covered = (360 + 140) m = 500 m.
∴ Required time = (500 x 2/25)sec = 40 sec.
Answer A
Answer: (A) 40 sec
Question: The concentration of spirit in three different vessels A, B and C are 45%, 30% and 10% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
(A) 26%
(B) 33%
(C) 34%
(D) 35%
(E) 24%
Rationale: Quantity of spirit in new solution=(4*45/100)+(5*30/100)+(6*10/100)=1.8+1.5+0.6=3.9 liters
So % concentration of spirit=100*3.9/(4+5+6)=26%
ANSWER:A
Answer: (A) 26%
Question: A water tank has two pipes to fill water in it. One of the pipes fills water at the rate of 100 litres per hour. The tank is filled by the other pipe in 6 hours and by both pipes together in 4.2 hours. What is the capacity of the tank in litres ?
(A) 860 litre
(B) 980 litre
(C) 1120 litre
(D) 1400 litre
(E) None of these
Rationale: Explanation:
Let the time taken by the 1st pipe to fill the tank be x hours.
When both the pipes are open, it is given that:
1/x + 1/6 = 1/(4.2) of tank is filled in 1 hour.
1/x + 1/6 = 5/21
21(6 + x) = 30 x
9x = 126
x = 14 hours
Therefore, capacity of the tank = 100 * 14 = 1400 litres.
ANSWER D
Answer: (D) 1400 litre
Question: A bowl was filled with 10 ounces of water, and 0.00008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.40%
(D) 4%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .00008 * 50
=.00008 * 100/2
= .008/2
= .004
percent of the original amount of water evaporated during this period = (.004/10) * 100%
= 0.04 %
Answer B
Answer: (B) 0.04%
Question: what is rate of interest if principal.amount be 400,simple interest 120 and time 2year.
(A) 10
(B) 12.5
(C) 25
(D) 12
(E) 15
Rationale: s.i=(p*r*t)/100
120=800r/100
r=120/8=15%
answer E
Answer: (E) 15
Question: How many 4-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 2 different consonants?
(A) 4!*5c2 *21c2
(B) 5P2 * 21P3 * 5!
(C) 5C2 * 21C3 * 5!
(D) 5P2 * 21P3
(E) 5C2 * 21C3
Rationale: combination for 2 vowels out of 5 =5c2 ways
combination for 2 consonants of 21 = 21c2 ways
Additionally the arrangement can be = 4!
total arrangements =4!*5c2 *21c2
A
Answer: (A) 4!*5c2 *21c2
Question: a student reached his school late by 20mins by travelling at a speed of 9kmph.if he had travelled at a speed of 12kmph,he would have reached his school 20mins early.what is the distance between house and school?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: distance = distance either student reaches school before time or after time
9(t+20/60) = 12(t-20/60)
i.e
9(t+1/3) = 12(t-1/3)
9(3t+1) = 12(3t-1)
t=7/3
put t value in any of distance equation
put t= 7/3 in 9(t+1/3)
we get 24 km
ANSWER:A
Answer: (A) 24
Question: A 6 litre sol is 30% alcohol .How many litres of pure alcohol must be added to produce a sol that is 50% alcohol ?
(A) A.0.6
(B) B.1
(C) C.2.1
(D) D.3
(E) E.2.4
Rationale: 30% of 6 = 1.8
50% of 6 = 3
shortage is 1.2
so we need to have 1.2/50% to get 50% alcohol content.
= 2.4 E
Answer: (E) E.2.4
Question: Rajesh can finish 1/3 of his home work in one hour. Seema can finish 3/7 of
her homework in 70 minutes and Ramya can finish 3/4 of her homework in
three and a quarter hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.00 PM for 30 minutes?
(A) 4:30pm
(B) 5:30pm
(C) 6:30pm
(D) 4:50pm
(E) 3:30pm
Rationale: ajesh can finish his work in 3 hr,
ramya can finish her work in 2.7 hr
seema can finish in 4.3 hr
so 4:50pm they can go to play
ANSWER:D
Answer: (D) 4:50pm
Question: Which of the following is a even number ?
(A) 9
(B) 11
(C) 4
(D) 3
(E) 1
Rationale: Explanation :
4 is a even number
Hence the even numbers are 2,4,6,8,10,12,14,... Answer : Option C
Answer: (C) 4
Question: in a certain tournament certain rules are followed: any player is eliminated the moment he losses for the third time (irrespective of how many wins he has), any player can play another player any number of times. If 512 contestants enter the tournament what is the largest number of games that could be played?
(A) 1535
(B) 1533
(C) 1536
(D) 1534
(E) 1556
Rationale: Explanation :
As there are 512 contestants , 511 contestants must be eliminated so that there can be only 1 winner.
In a single match there is only 1 loss and for elimination of a contestant he must lose 3 matches;
therefore for eliminating 511 contestants , the nos of matches required is : 511 x 3 = 1533
The last contestant i.e the winner can also lose a maximum of 2 matches.
So the maximum nos of games that could be played is 1533+2 = 1535
Answer : A
Answer: (A) 1535
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600
(D) 9670
(E) 9800
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600. Answer: Option C
Answer: (C) 9600
Question: Amul's Ice Cream Shop sells ice cream at a cents a scoop. For an additional b cents, a customer can add 7 toppings to his or her sundae. How much would a sundae with 7 scoops and 7 toppings cost, in terms of a and b?
(A) 7a+2b
(B) 7a+b
(C) 6a+b
(D) 5a+b
(E) 5a+3b
Rationale: Answer B 7a+b
Answer: (B) 7a+b
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 50 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 40 km/h. If the distance between City P and City Q is 230 km, at what time will the truck and the car meet each other?
(A) 4:00
(B) 4:30
(C) 5:00
(D) 5:30
(E) 6:00
Rationale: At 2:00 pm, the truck and the car are 180 km apart.
The truck and the car complete a distance of 90 km each hour.
The time it takes to meet is 180/90 = 2 hours.
They will meet at 4:00 pm.
The answer is A.
Answer: (A) 4:00
Question: A train 450 m long running at 108 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 271
(B) 266
(C) 350
(D) 277
(E) 300
Rationale: Length of the platform = 108 * 5/18 * 25 = 750 – 450
= 300
Answer:E
Answer: (E) 300
Question: A set consist of 2m-1 element. What is the number of subsets of this set which contain at most m-1 elements?
(A) 2^(2m-2)
(B) 2^(2m) - 2
(C) 2^(2m) -1
(D) 2^(2m)
(E) 2^(2m-1)
Rationale: I used m=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
Avoid 2 since you will get 1 arrangement (m-1) and may be risky since 1 is a number with certain unique properties
Answer: (A) 2^(2m-2)
Question: A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
(A) 7/2 kmph
(B) 8/2 kmph
(C) 5/2 kmph
(D) 1/2 kmph
(E) 2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-9)/2 = 1/2 km/hr.
Answer: D
Answer: (D) 1/2 kmph
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long K would it have taken for him to walk both ways.
(A) 8 h 45 min
(B) 7 h 45 min
(C) 6 h 45 min
(D) 5 h 30 min
(E) None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back K=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: (A) 8 h 45 min
Question: Set W includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First, reach to the point of getting the equation W: x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: (D) 3
Question: A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $420 less than the sum lent. What was the sum lent?
(A) 500
(B) 600
(C) 700
(D) 800
(E) 900
Rationale: P - 420 = (P*5*8)/100
P = 700
The answer is C.
Answer: (C) 700
Question: Departments A, B, and C have 6 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible?
(A) 19,000
(B) 41,040
(C) 100,000
(D) 190,000
(E) 400,000
Rationale: 6c1 * 6c1* 6c1*20c2 = 6*6*6*190=41,040. Hence B is the correct answer.
Answer: (B) 41,040
Question: An investor invests in a new fund. The fund averages 10% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
(A) 97.64%
(B) 100.98%
(C) 103.45%
(D) 106.48%
(E) 109.78%
Rationale: 0.8*1.1^3 = 1.0648
The answer is D.
Answer: (D) 106.48%
Question: Which of the following is closest to (-2/3)^199？
(A) -1
(B) -1/2
(C) 0
(D) 1
(E) 2
Rationale: (-2/3)^4 = 16/81 which is already less than 1/2.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Answer: (C) 0
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. a-c=-2
II. abc is an even integer
III. (a+b+c)/3 is an integer
(A) All are correct
(B) II
(C) I and II
(D) II and III
(E) None are correct
Rationale: 1. a-c=-2 --> a, b, c are consequitive positive integers and a<b<c then c=a+2 --> a-c=2. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: A.
Answer: (A) All are correct
Question: E is the midpoint of AC in right triangle ABC shown above. If the area of ΔABC is 24, what is the area of ΔBED?
A.
B.
C.
D.
E.
(A) 9√3
(B) 9√2
(C) 12
(D) 9
(E) 6√2/3
Rationale: Since BE is the median, Area of triangle ABE = Area of triangle EBC = 1/2 * Area of triangle ABC = 12.
Also, since Angle C = 45, AB = AC.
But, 1/2 * AB*AC = 24 => AC = \sqrt{48} = 4\sqrt{3}
AE = AC/2 = 2\sqrt{3}
Now, triangle EDC is again right angled. so area of triangle EDC = 1/2 * ED * DC .
But ED = DC and ED^2 + DC^2 = 12 => ED = \sqrt{6}
So area of triangle EDC = 1/2 *\sqrt{6} *\sqrt{6} = 3
Now area of triangle BCD = Area of triangle EBC - Area of triangle EDC => 12 -3 = 9.
ANSWER:D
Answer: (D) 9
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 768
(B) 268
(C) 260
(D) 480
(E) 269
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: (D) 480