mathewhe/aqua_rat huggingface dataset:
Question: Look at this series: 75, 75, 70, 70, 65, 65, ... What number should come next?
(A) 14
(B) 15
(C) 17
(D) 60
(E) 11
Rationale: In this series, each number is repeated, then 5 is subtracted to arrive at the next number.
The next number is 60
Answer : D
Answer: (D) 60
Question: If x is a positive integer less than 30, is 'x' an odd number?
(A) 87
(B) 65
(C) 77
(D) 56
(E) 19
Rationale: Answer:B
Answer: (B) 65
Question: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. What is the remainder when nm is divided by 9?
(A) 4
(B) 2
(C) 3
(D) 0
(E) 1
Rationale: n = 9x + 6
m = 12y + 4
nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/9 = (108xy + 36x + 72y + 24)/9
Observe that the all four terms are a multiple of 9
hence nm is divisible by 9
Correct Option: D
Answer: (D) 0
Question: A man can row with a speed of 5 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?
(A) 29
(B) 35
(C) 20
(D) 27
(E) 121
Rationale: M = 5
S = 30
DS = 5 + 30 = 35
Answer: B
Answer: (B) 35
Question: 120 is what percent of 40 ?
(A)  5%
(B)  20%
(C)  50%
(D)  300%
(E)  500%
Rationale: 40*x=120 --> x=3 --> 3 expressed as percent is 300%.
Answer: D.
Answer: (D)  300%
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
(A) 20
(B) 22
(C) 24
(D) 48
(E) 45
Rationale: Solution
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Answer B
Answer: (B) 22
Question: The average age of 3 boys is 20 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?
(A) 10years
(B) 15years
(C) 20years
(D) 25years
(E) 12years
Rationale: Total age of 3 boys = 20*3 = 60
ratio of their ages = 3:5:7
Age of the youngest = 60*3/15 = 12 years
Answer is E
Answer: (E) 12years
Question: A cycle is bought for Rs.675 and sold for Rs.1080, find the gain percent?
(A) 22
(B) 60
(C) 99
(D) 88
(E) 11
Rationale: 675 ---- 180
100 ---- ? => 60%
Answer:B
Answer: (B) 60
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 4 hours?
(A) 125 miles
(B) 225 miles
(C) 260 miles
(D) 425 miles
(E) 525 miles
Rationale: During each hour, the car travels 65 miles. For 4 hours it will travel
65 + 65 + 65 + 65 = 4 × 65 = 260 miles
correct answer is C) 260 miles
Answer: (C) 260 miles
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
(A) Rs. 207.40
(B) Rs. 534.60
(C) Rs. 648
(D) Rs. 655.60
(E) Rs. 555
Rationale: Explanation:
Number of shares =4455/8.25 =540
Face value = Rs. (540 x 10) = Rs. 5400.
Annual income = Rs. 12/100*5400 =Rs. 648
ANSWER IS C
Answer: (C) Rs. 648
Question: Praveen starts business with Rs.3220 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
(A) s.7500
(B) s.8000
(C) s.8280
(D) s.9000
(E) s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3220 * 12/7x = 2/3
=> 14x = 115920
=> x =8280.
ANSWER:C
Answer: (C) s.8280
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 210m
(B) 240m
(C) 963m
(D) 874m
(E) 578m
Rationale: Explanation:
Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B)240m
Answer: (B) 240m
Question: If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/3 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
(A) 5/3
(B) 5/4
(C) 10/3
(D) 15/4
(E) 15/2
Rationale: N = 2D/5
J = N/3 = 2D/15
The average of November and January is (N+J)/2 = 8D/15 / 2 = 4D/15
D is 15/4 times the average of November and January.
The answer is D.
Answer: (D) 15/4
Question: If x≠6 and (x^2 - 36)/(2y) = (x - 6)/4, then in terms of y, x = ?
(A) (y - 6)/2
(B) (y - 3)/2
(C) y - 3
(D) (y - 12)/2
(E) (y + 6)/2
Rationale: Since (x^2 – 36)=(x-6)(x+6) the original equation can be changed into 4*(x-6)(x+6) = 2y *(x-6).
By cancelling 2(x-6) (we can do it because x≠6) we get :
2*(x+6)=y.
So x=(y-12)/2. So the answer is D).
Answer: (D) (y - 12)/2
Question: How many 4 digit odd numbers do not use any digit more than once
(A) 1720
(B) 2160
(C) 224
(D) 2460
(E) None of these
Rationale: The Way i solved it is
A B C D ( thousand , hundreds, tens, units)
D can be 1 3 5 7 9 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
C can be anything execpt A and B so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 8 * 7 * 8 * 5 = 2240
Ans E
Answer: (E) None of these
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
(A) 5
(B) 6
(C) 8
(D) 7
(E) 9
Rationale: Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9.30 a.m.
ANSWER:D
Answer: (D) 7
Question: In a colony of 70 residents, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
(A) 1:9
(B) 1:6
(C) 1:3
(D) 1:1
(E) 1ratio 3
Rationale: Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer: E
Answer: (E) 1ratio 3
Question: The population of a town increase annually by 20% . If the present population is 2,00,000, then what is the difference in population after two years and three years
(A) 63,250
(B) 48,800
(C) 60,800
(D) 57,600
(E) 67,600
Rationale: M .F for 2Yrs = 120/100*120/100 =36/25
M .F for 3Yrs =120/100*120/100*120/100 =6/5*6/5*6/5 =216/125
Population after 2Yrs = 2,00,000*36/25 = 2,88,000
Population after 3 Yrs = 2,00,000*216/125 = 3,45,600
Difference = 3,45,600 – 2,88,000 =57,600
ANSWER:D
Answer: (D) 57,600
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered?
(A) 28.5
(B) 27.675
(C) 30
(D) Data inadequate
(E) None of these
Rationale: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100×(100+23.5)/(100−5)
= 100×247/190=130
Hence, required % Profit = 130 – 100 = 30%
Answer C
Answer: (C) 30
Question: The C.P of 8 books is equal to the S.P of 16 books. Find his gain% or loss%?
(A) 60%
(B) 50%
(C) 70%
(D) 90%
(E) 55%
Rationale: explanation:
8 CP = 16 SP
16 --- 8 CP loss
100 --- ? => 50% loss
Answer: B
Answer: (B) 50%
Question: A train is running at a speed of 4040 km/hr and it crosses a post in 1818 seconds. What is the length of the train?
(A) 190 metres
(B) 160 metres
(C) 200 metres
(D) 120 metres
(E) 150 metres
Rationale: Explanation:
Speed =40 km/hr =40 km/hr =40Ã—518=1009 m/s=40Ã—518=1009 m/s
Time =18=18 seconds
Distance Covered =1009Ã—18=200 m=1009Ã—18=200 m
Therefore, length of the train =200 m
ANSWER IS C
Answer: (C) 200 metres
Question: You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.
How can you do it?
Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature.
(A) 45 minutes
(B) 40 minutes
(C) 35 minutes
(D) 55 minutes
(E) 60 minutes
Rationale: A
45 minutes
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.
Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.
Answer: (A) 45 minutes
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 23
(B) 27
(C) 28
(D) 12
(E) 25
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:D
Answer: (D) 12
Question: List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 12
Rationale: Answer = C =7
If least = -3, then largest = 8
Range = 8 - 1 = 7
Answer: (C) 7
Question: A train running at the speed of 162 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 286 meter
(C) 186 meter
(D) 405 meter
(E) 265 meter
Rationale: Speed = 162*(5/18) m/sec
= 45 m/sec
Length of Train (Distance)
= Speed * Time
(45) * 9 = 405 meter
Answer:D
Answer: (D) 405 meter
Question: Which of these following integers is the square of an integer?
(A) 49981101542
(B) 49206101137
(C) 49471101241
(D) 49859101723
(E) 49323101988
Rationale: The unit digit of any perfect square can not be 2, 3, 7, or 8.
The answer is C.
Answer: (C) 49471101241
Question: A soccer store typically sells replica jerseys at a discount of 60 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 50
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, E is the answer
Answer: (E) 50
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 3 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R = 1/36
Rate of machine S = 1/18
Rate of R+S = 1/12
To finish the work in 3 hrs, the combined rate needs to be 1/3.
x * 1/12 = 1/3
x = 4
The answer is B.
Answer: (B) 4
Question: One-seventh of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/15 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
(A) 2.3%
(B) 3.4%
(C) 4.5%
(D) 5.6%
(E) 6.7%
Rationale: 1/7 of the switches are defective.
The defective switches that are not rejected are 1/5*1/7 = 1/35 = 3/105 of all switches.
The non defective switches that are sold are 6/7*14/15 = 84/105 of all switches.
The percent of switches sold that are defective is 3/87 which is about 3.4%.
The answer is B.
Answer: (B) 3.4%
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 30 as remainder
(A) 1235
(B) 1456
(C) 1567
(D) 1632
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 30
5x = 1335
x = 267
Large number = 267+1365 = 1632
D
Answer: (D) 1632
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
(A) 10 cm
(B) 20 cm
(C) 30 cm
(D) 40 cm
(E) 50 cm
Rationale: Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 5) - 2x * x = 75 <=> 5x - 25 = 75 <=> x = 20.
:. Length of the rectangle = 20 cm.
ANSWER B 20 cm
Answer: (B) 20 cm
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 150 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 39
(B) 27
(C) 36
(D) 88
(E) 12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 150 = 390 m.
Time taken = 390/10 = 39 sec.
Answer: A
Answer: (A) 39
Question: Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at constant rate that is 2 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from the original destination has Heather walked when the two meet?
(A) 5miles
(B) 7 miles
(C) 9 miles
(D) 10 miles
(E) 12 miles
Rationale: Original distance between S and H = 20 miles.
Speed of S = 5+2 = 7 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+24/60 = t+2/5 hours.
Now, the total distances traveled by S and H = 20 miles ---> 7*(t+2/5)+5*t=20 ---> t= 86/60 hours. Thus H has traveled for 86/60 hours giving you a total distance for H = 5*86/60 = 7 miles.
B is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: (B) 7 miles
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 80 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
(A) 8:5
(B) 9:25
(C) 5:8
(D) 25:9
(E) Cannot be determined from the information provided
Rationale: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*40/Speed B
Since the times are same,
50pi/Speed A = 80pi/Speed B
SpeedA/Speed B = 50pi/80pi = 5/8
Correct Option: C
Answer: (C) 5:8
Question: By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 20?
(A) Not possible
(B) 9
(C) 4
(D) 6
(E) 8
Rationale: A number to be divisible by 50 must end with 00 or 50.
So, not possible.
Answer: A.
Answer: (A) Not possible
Question: Kamal obtained 76, 60, 82, 67 and 85 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 65
(B) 69
(C) 74
(D) 75
(E) NOne
Rationale: Sol.
Average
= 76 + 60 + 82 + 67 + 85 / 5)
= (375 / 5)
= 74.
Answer C
Answer: (C) 74
Question: If 15% of A is the same as 20% of B, then A : B is :
(A) 3 : 4
(B) 4 : 3
(C) 17 : 16
(D) 16 : 17
(E) None of these
Rationale: Expl : 15% of A I= 20 % of B =15A/100 = 20B/100 = 4/3 = 4:3
Answer:B
Answer: (B) 4 : 3
Question: Tom wants to buy items costing $25.35, $50.69, and $95.96. He earns $6.50 an hour doing
odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he
work to earn the money he needs for his purchases? Round your answer to the nearest whole
hour.
(A) 29 hours
(B) 48 hours
(C) 38 hours
(D) 18 hours
(E) 28 hours
Rationale: $6.50 x .10 = $.65 is 10% of his hourly income
$6.50 - .65 = $5.85 hourly amount available to spend
$25.35 + $50.69 + $95.96 = $172 total needed
$172 ÷ $5.85 = 29.4... rounds to 29 hours
correct answer A
Answer: (A) 29 hours
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 500 more than D, what is B's share?
(A) A)8239
(B) B)2900
(C) C)1000
(D) D)2393
(E) E)2009
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 500 => x = 500.
B's share = Rs. 2x = 2 * 500 = Rs. 1000.
Answer: C
Answer: (C) C)1000
Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:
(A) 1:1
(B) 1:2
(C) 1:3
(D) 1:4
(E) 1:6
Rationale: A square and a rhombus on the same base are equal in area Answer: A
Answer: (A) 1:1
Question: 500 is increased by 30%. Find the final number.
(A) 550
(B) 500
(C) 650
(D) 600
(E) 700
Rationale: ExplanationFinal number = Initial number + 30%(original number) = 500 + 30%(500) = 500 + 150 = 650.Answer C
Answer: (C) 650
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) 288
(B) 132
(C) 772
(D) 592
(E) 261
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
Answer: B
Answer: (B) 132
Question: If the President and Vice President must sit next to each other in a row with 4 other members of the Board, how many different seating arrangements are possible?
(A) 120
(B) 240
(C) 300
(D) 360
(E) 720
Rationale: We need to take President and VP as one unit. Therefore we have 5 people to arrange=5! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=5!*2!=240 ways
Answer B
Answer: (B) 240
Question: Find the average of first 10 natural numbers.
(A) A)10.5
(B) B)9.9
(C) C)7.5
(D) D)6.6
(E) E)5.5
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 10 natural numbers = 10*11/2 =55
average = 55/10 = 5.5
Answer is E
Answer: (E) E)5.5
Question: A store sells four different kinds of shirts. If we want to buy two different kinds of shirts, how many possible combinations of two shirts can we buy?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 4C2=6.
The answer is B.
Answer: (B) 6
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 30
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: Option C
Answer: (C) 36
Question: A train covers a distance of 12 km in 5 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 120m
(B) 180m
(C) 240m
(D) 220m
(E) 280m
Rationale: Speed = (12/5 * 60) km/hr = (144 * 5/18) m/sec = 40 m/sec.
Length of the train = 40 * 6 = 240 m.
ANSWER:C
Answer: (C) 240m
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 36 ?
(A) 440
(B) 512
(C) 550
(D) 620
(E) 750
Rationale: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 36 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 36)
Answer (D)
Answer: (D) 620
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 30 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 97%
(C) 100%
(D) 105%
(E) 120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.3 = 39
B = 20*1.5*1.3 = 39
C = 20*1.5*0.4 = 12
D = 20*0.6*1.25 = 15
E = 0
Total 39 + 39 + 12 + 15 = 105.
Answer: D.
Answer: (D) 105%
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
(A) 2160
(B) 2162
(C) 2161
(D) 2163
(E) 2134
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Answer A.
Answer: (A) 2160
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses R at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) R=256
(D) R=384
(E) R=480
Rationale: Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: (E) R=480
Question: There are 9 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
(A) 15
(B) 16
(C) 28
(D) 56
(E) 72
Rationale: Every team plays with 8 teams...so total no of matches = 9 x 8 = 72.
Now, each match is played twice => 72 x 2
But 2 teams play a match => 72 x 2 /2 = 72.
Answer: E
Answer: (E) 72