divelab/Sys2Bench huggingface dataset:
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 T at the restaurant? (Assume that all boxes are filled to capacity.)
Options:
A)96
B)240
C)T=256
D)T=384
E)T=480
Rationale: Most Test Takers would recognize the system of 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
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $400 before any discount?
Options:
A) $230.00
B) $224.00
C) $263.80
D) $282.00
E) $210.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $400 would be.....
($400)(.7)(.8) =
($400)(.56)=224
Final Answer:
B
Answer: B
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 20 hrs and a machine of type S does the same job in 30 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Type R completes 1/20 of the job each hour.
Type S completes 1/30 of the job each hour.
Together R and S complete 1/20 +1/30 = 1/12 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/12) = 1 job completed
n = 6
The answer is C.
Answer: C
Question: A letter lock consists of three rings each marked with nine different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)176
B)178
C)728
D)789
E)770
Rationale: Since each ring consists of nine different letters, the total number of attempts possible with the three rings is
= 9 * 9 * 9= 729. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 729 - 1 = 728.
Answer: C
Answer: C
Question: How many words can be formed using the letters of the word “COMPANY”?
Options:
A)1224
B)2434
C)3243
D)3435
E)5040
Rationale: There are ‘7’ different letters of the word “COMPANY”
Number of Permutations taking all the letters at a time = 7P7
7!= 5040
E
Answer: E
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Options:
A)6 months
B)8 months
C)9 months
D)10 months
E)15 months
Rationale: TD=Amt*R*T/(100+RT)
given TD=160,Amt=1760,R=12,T=?
by substituting the values we get,
160=(1760*12T)/(100+12T)
160(100+12T)=1760*12T
100+12T=(1760*12T)/160
100+12T=132T
120T=100
t=100/120=5/6yrs i.e (5/6)*12=10months
ANSWER:D
Answer: D
Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.
Options:
A)170
B)179
C)37
D)67
E)32
Rationale: Divisor = (Dividend – Remainder/Quotient)
=(15968-37)/89 =179
ANSWER B 179
Answer: B
Question: For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 6*+2 and 6*+6, inclusive ?
Options:
A)1
B)None of the above
C)2
D)3
E)4
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6* + 2 = 6! + 2 and 6* + 6 = 6! + 6.
Now, notice that we can factor out 2 our of 6! + 2 so it cannot be a prime number, we can factor out 3 our of 6! + 3 so it cannot be a prime number, we can factor out 4 our of 6! + 4 so it cannot be a prime number, ... The same way for all numbers between 6! + 2 and 6! +7, inclusive. Which means that there are no primes in this range.
Answer: B
Answer: B
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
Options:
A)90 sec
B)75 sec
C)85 sec
D)80 sec
E)None of these
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
ANSWER:A
Answer: A
Question: Two cars cover the same distance at the speed of 32 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)73
B)38
C)64
D)83
E)93
Rationale: Explanation:
32(x + 1) = 64x
X = 1
32 * 2 = 64 km
Answer: Option C
Answer: C
Question: The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg. What is the weight of the new person?
Options:
A)75 kg
B)85 kg
C)95 kg
D)65 kg
E)105 kg
Rationale: The total weight increase = (8 x 2.5) kg = 20 kg
weight of new person = (85 + 20) kg = 105 kg
The answer is E.
Answer: E
Question: A Steel 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 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Options:
A)3
B)4
C)6
D)9
E)12
Rationale: Rate of machine R =1/24
Rate of machine S =1/12
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/24 +x/12 =1/2
3x/24=1/2
x=24/6=4
So no of machine R is 4
Answer B
Answer: B
Question: Of the integers between 200 and 799, inclusive, how many do not have digit 2 and 7?
Options:
A) 256
B) 326
C) 410
D) 426
E) 520
Rationale: Options for the first digit 6-2(2 and 5)=4;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 4*8*8=256.
Answer: A.
Answer: A
Question: 3x^2-6x+3 = 0 Find the above equation find the value of x
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
Answer: B
Question: In a parallelogram, the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively. Find its area
Options:
A)600 m2
B)540 m2
C)680 m2
D)574 m2
E)None of these
Rationale: In a parallelogram.
Area = Diagonal × length of perpendicular on it.
= 30 × 20 = 600 m2
Answer A
Answer: A
Question: The average of 7 numbers is 24. If each number be multiplied by 5. Find the average of new set of numbers?
Options:
A)110
B)122
C)120
D)125
E)145
Rationale: Explanation:
Average of new numbers = 24 * 5 = 120
Answer: Option C
Answer: C
Question: In a college election between two rivals, a candidate who got 40% of the total votes polled, was defeated by his rival by 160 votes. The total number of votes polled was
Options:
A)900
B)800
C)700
D)600
E)None of these
Rationale: Let total number of votes polled be x.
Then, votes polled by other candidate
= (100 – 40)% of x = 60% of x
Now 60% of x – 40% of x = 160
⇒ 20x⁄100 = 160 ⇒ x = 800 votes
Answer B
Answer: B
Question: Krishan and Nandan jointly started a business. Krishan invested four times as Nandan did and invested his money for trible time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs.26000, find the Nandan's earning.
Options:
A)4000
B)1000
C)5000
D)3000
E)2000
Rationale: 4:1
3:1
------
12:1
13 ----- Rs.26000
1 ----- ? => Rs.26,000/13=Rs. 2000
Answer: E
Answer: E
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $44. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)xy/360
B)9xy/40
C)40xy/9
D)396xy
E)396/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 44 / (xy/9) = 396/(xy).
The answer is E.
Answer: E
Question: The ratio of two speeds of two trains is 3 to 4. If each of the trains slows its speed 5 km/ hr, what will be the ratio of these two train speeds ?
Options:
A)3/4
B)8/9
C)18/19
D)23/24
E)It cannot be determined from the information given
Rationale: 3/4 = 3x/4x
we need to find out (3x+5)/(4x+5) off course we cannot solve this to arrive at any rational number hence E.
Answer: E
Question: The number obtained by interchanging the two digits of a two-digit number is less than the original number by 45. If the sum of the two digits of the number so obtained is 13, then what is the original number?
Options:
A)94
B)66
C)39
D)87
E)58
Rationale: A
94
Let the number be in the form of 10a + b
Number formed by interchanging a and b = 10b + a.
a + b = 13 --- (1)
10b + a = 10a + b - 45
45 = 9a - 9b => a - b = 5 --- (2)
Adding (1) and (2), we get
2a = 18 => a = 9 and b = 4
The number is: 94.
Answer: A
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 55 percent of the pack would be outfielder cards?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 55% of toatal Ocards
12-X<.55*12
X<12-6.6
X<5.4
X=5
Ans B
Answer: B
Question: A man can row upstream at 20 kmph and downstream at 80 kmph, and then find the speed of the man in still water?
Options:
A)32 kmph
B)50 kmph
C)30 kmph
D)45 kmph
E)65 kmph
Rationale: US = 20
DS = 80
M = (20 + 80)/2 = 50
Answer:B
Answer: B
Question: In an office, 30 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Options:
A) 480
B) 48
C) 50
D) 144
E) 160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(30/100)*Workers = x+16 = > x = 48
Answer B
Answer: B
Question: 9.5 , 9.8 , 9.9 , 9.9 , 9.9 , 10.2 , 10.3 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.296 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
Options:
A)90.75%
B)85.60%
C)80%
D)75.25%
E)62.5%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.296; 10+0.296} = {9.704; 10.296}.
From the 8 listed numbers, 5 are within this range so 5/8=62.5%.
Answer: E.
Answer: E
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)5
B)8
C)1
D)6
E)1.5
Rationale: Explanation:
M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: E
Answer: E
Question: A,B,C can complete a piece of work in 24,8,12 days. Working together, they complete the same work in how many days?
Options:
A)4
B)4/5
C)7/9
D)10
E)24/7
Rationale: A+B+C 1day work = 1/24 + 1/8 + 1/12 = 6/24 = 1/4
A,B,C together will complete the job in 4 days
Answer is A
Answer: A
Question: The sum and the product of two numbers are 16 and 15 respectively, the difference of the number is?
Options:
A)14
B)6
C)7
D)8
E)2
Rationale: Explanation:
x + y = 16
xy = 15
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 256 - 60 => (x - y) = 14
Answer: A
Answer: A
Question: In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 17 years replaced by a new boy. The age of the new boy is?
Options:
A)14 years 8 months
B)15 years
C)13 years 8 months
D)17 years 10 months
E)17 years
Rationale: Total decrease = (20 x 2) months
= 3 years 4 months
Age of the new boy
= 17 years - 3 years 4 months.
= 13 years 8 months.
ANSWER:C
Answer: C
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 55% play football, how many play both?
Options:
A)120
B)150
C)200
D)180
E)160
Rationale: n(A) = 75*600/100 = 450
n(B) = 55*600/100 = 330
n(AUB) = 600
n(AnB) = 450+330-600 = 180
Answer is D
Answer: D
Question: A certain team consists of 3 professors and 6 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
Options:
A)48
B)52
C)56
D)60
E)64
Rationale: The total number of ways to form a group of 3 from 9 people is 9C3 = 84
The number of ways to form a group without a professor is 6C3 = 20
The total number of ways to form a valid group is 84 - 20 = 64.
The answer is E.
Answer: E
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
Options:
A)1/2
B)2/3
C)3/5
D)3/7
E)3/8
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: A
Question: A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?
Options:
A)48
B)36
C)72
D)60
E)120
Rationale: No. of ways the 5 digit number can be formed = 5! = 120
Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48
No. of ways 1 & 2 wont be together = 120 - 48
=72
ANSWER:C
Answer: C
Question: A certain number X when divided by 253 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?
Options:
A)17
B)27
C)27
D)47
E)57
Rationale: Least possible value of the number is 253 + 98 = 351
Further it is given the number must be divisible by 81 .
351/81 = Gives remainder as 27
So, 27 must be subtracted from the number , answer is (C)
Answer: C
Question: During a Pizza buffet where A eats more times 2.4 than B, and B eats 6 times less than C.find the leat number of times all the three has to eat
Options:
A)50
B)60
C)70
D)80
E)85
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.4:1 or 12:5 and as B eat 6 times less the C the the ratio of B : C is 5:30 the the least number of times all three has eat is the LCM of A,B,C that is 60 ..
ANSWER:B
Answer: B
Question: X and Y together can completes a work in 12 days and Y complete the same work in 24 days. Then the number of days X required to complete the work will be?
Options:
A)15 days.
B)12 days.
C)24 days.
D)13 days.
E)16 days.
Rationale: X and y complete in one day =1/12 part, y completes in one day=1/24 parts. Therefore X alone can do in one day =1/24part. Therefore the work can be finished by X = 24 days. Ans: C
Answer: C
Question: If the average (arithmetic mean) of a and b is 215, and the average of b and c is 160, what is the value of a − c?
Options:
A)−220
B)−100
C)100
D)110
E)It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =215 ===> a + b = 430
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) =430- 320 ===> a + b - b - c = 110 ===> a - c = 110
Answer: D
Answer: D
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?
Options:
A)22377
B)27000
C)27891
D)25000
E)18771
Rationale: 27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
27 = 1/1000 * x => x = 27000
Answer: B
Answer: B
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 20 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
Options:
A)32 lakh
B)50 lakh
C)40 lakh
D)60 lakh
E)None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+20/8x=5/4 ⇒ 20x + 80 = 40x
∴ x = 4
∴ Income of company B = 8x = 32 lakh
Answer A
Answer: A
Question: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 8 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?
Options:
A)30
B)20
C)18
D)12
E)6
Rationale: 21-12 < no of hrs < 21-8
9< no of hrs < 13.
D
Answer: D
Question: Meera is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Meera must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
Options:
A)75
B)150
C)300
D)3600
E)7,500
Rationale: I'd use backsolving for this question.
Check D:
3600 lenses = 1800 usable lenses = 900 tubes = 900 eyepieces. We CAN buy 900 tubes and 900 eyepieces, so that not to have leftovers.
Answer: D.
Answer: D
Question: Which of the following expressions CANNOT have a negative value
Options:
A)|a + b| – |a – b|
B)|a + b| + |a|
C)|2a + b| – |a + b|
D)a^2 - b^2 – 2|ab|
E)|a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
|a + b| + |a|
This will always be positive.
Correct Option: B
Answer: B
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 210 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)1120
B)672
C)560
D)192
E)1680
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 30hrs. hence, possible scenarios, if
(1)2x =210 => 16x = 1680 (2) 3x =210 => 16x = 1120 (3) 5x =210 => 16x = 672 (4) 6x =210 => 16x = 560
Hence Answer is D 192 which can not be any of these.
Answer: D
Question: On Wednesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
Options:
A)Tuesday
B)Wednesday
C)Thursday
D)Friday
E)Sunday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Wednesday, 3rd day is Saturday. Next day, which he won't have a new combination for, is Sunday. (E)
Answer: E
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is?
Options:
A)4:6
B)4:3
C)4:9
D)4:4
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš16 : âˆš4 = 4:2.Answer: E
Answer: E
Question: 26 : 62 :: 32:?
Options:
A)49
B)25
C)36
D)64
E)23
Rationale: Ans 23
Reverse of 32
ANSWER:E
Answer: E
Question: What least number must be subtracted from 9671 so that the remaining number is divisible by 5?
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: On dividing 9671 by 5, we get remainder = 1.
Required number be subtracted = 1
ANSWER:E
Answer: E
Question: Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1135
B)B)1075
C)C)1065
D)D)1070
E)E)1080
Rationale: Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
A)
Answer: A
Question: A property was originally on a 99 years lease and two thirds of the time passed is equal to the four fifth of the time to come.how many years are there to go.
Options:
A)33
B)80
C)79
D)27
E)111
Rationale: Answer:B
Answer: B
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 40% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
Options:
A)$20
B)$40
C)$50
D)$80
E)$60
Rationale: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 40%, so the manufacturing must have been $60. Answer = (E).
Answer: E
Question: Find out the square of a number which when doubled exceeds its one sixth by 11 ?
Options:
A)36
B)25
C)19
D)26
E)17
Rationale: A
Let the number be p, then the square will be p^2
According to question:
2p = (p/6) + 11
=> 12p = p + 66
=> p = 6
p^2 = 6^2 = 36.
Answer : A
Answer: A
Question: A dinner has 2 coffee pitchers; Each can hold 8 cups of coffee. During Monday's morning rush, a customer orders 10 cups of coffee. At the time this customer orders the coffee, one coffee pitcher is 1/4 full while the other is 3/8 full. How much of the customer's order can be filled without making more coffee.
Options:
A)1/3
B)5/8
C)3/4
D)2/3
E)1/2
Rationale: One pitcher has 2 cups of coffee and the other has 3 cups of coffee. This means there is a total of 5 cups of coffee. That means 5 of the 10 cups of coffee can be given to the customer before the dinner makes more coffee. 5/10 simplifies to 1/2. (Answer: E)
Answer: E