divelab/Sys2Bench huggingface dataset:
Question: If p and q are two different odd prime numbers, such that p < q, then which of the following must be true?
Options:
A)(2p + q) is a prime number
B)p + q is divisible by 4
C)q - p is divisible by 4
D)(p + q + 1) is the difference between two perfect squares of integers
E)p2+q2 is the difference between two perfect squares of integers
Rationale: 1. (2p + q) for sure is an odd number , but may or may not be a prime number .
Eg - if we take 3 and 5 as p and q resp, we get 11, which is a prime number.
But if we take 7 and 11, we get 25, which is not a prime number.
2. p + q for sure gives us an even number. It may or may not be divisible by 4.
Eg - (7 + 5) = 12 , which is divisible by 4. But (11 + 7) = 18 , not divisible by 4
3. Same way as 2nd.
4. (p + q + 1) gives us an odd number.
Lets see the trend of difference between squares of consecutive integers.
2^2 - 1^2 = 3
3^2 - 2^2 = 5
4^2 - 3^2 = 7
5^2 - 4^2 = 9
6^2 - 5^2 = 11 and so on.
The trend is : The difference between squares of consc. integers is always odd number. And it covers all the odd numbers.
However , when we don't take consecutive integers, this trend is not followed.
Eg : 5^2 - 3^2 = 16 , which is an even number
3^2 - 1^2 = 8 , again not an odd number
Hence : Any odd number can be expressed as the difference of the squares of integers.
5. (p^2 + q^2) gives an even number.
ANSWER:D
Answer: D
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 5 consecutive integers that start with (m + 2)?
Options:
A)m + 3
B)n + 6
C)n + 3
D)m + 5
E)n + 2
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 5 consecutive numbers starting from n is n+2.
The answer is E.
Answer: E
Question: If 0 < p < 1 < q< 5, which of the following must be less than 1? I. p/q II. pq III. q - p
Options:
A)III only
B)II only
C)I only
D)II,III only
E)I,III only
Rationale: q > 1. So, option II, III is not possible.
So, Option I is correct.
Answer : C
Answer: C
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $14, what was the price before the first discount?
Options:
A)$45.10
B)$34.31
C)$24.88
D)$67.54
E)$65.23
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 14
(x - 25%x) - 25%(x - 25%x) = 14
Solve for x
x = $24.88
correct answer C
Answer: C
Question: In a games hour 4 different types of players came to the ground? cricket 12, hokey 17, football 11, softball 10. How many players are present in the ground?
Options:
A)70
B)50
C)62
D)49
E)50
Rationale: total number of players= 12+17+11+10= 50
Answer is B
Answer: B
Question: A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
Options:
A)126
B)277
C)188
D)171
E)181
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
8C_{3}+8C_{4}}=56 + 70= 126
Answer: A
Answer: A
Question: The ages of two person differ by 20 years. If 7 years ago, the elder one be 5 times as old as the younger one, their present ages(in years) are respectively
Options:
A)30, 10
B)32, 12
C)29, 9
D)50, 30
E)20,10
Rationale: Let their ages be x and (x + 20) years.
Then, 5(x - 7) = (x + 20 - 7)
=> 4x = 48
=>x =12
Their present ages are 32 years and 12 year.
ANSWER:B
Answer: B
Question: Peter has 9 candies, rina has 5 candies. Totally how many candies they have in all?
Options:
A)14
B)4
C)23
D)12
E)9
Rationale: 9+5=14. Answer is A
Answer: A
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of five specified novels, and choose two plays from a list of 6 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
Options:
A)55
B)60
C)65
D)70
E)75
Rationale: 5C1*6C2 = 5*15 = 75
The answer is E.
Answer: E
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
Options:
A)14%
B)15%
C)25%
D)30%
E)35%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: C
Question: 11, 10, ?, 100, 1001, 1000, 10001
Options:
A)1000
B)121
C)111
D)101
E)91
Rationale: The pattern is - 1, × 10 + 1, - 1, × 10 + 1, - 1, × 10 + 1, ....
Answer : D.
Answer: D
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = -a
|b - 6| + |ab - b| = ?
Options:
A)a) ab - 2b + 6
B)b) 2b - ab - 4
C)c) ab + 4
D)d) ab - 2b + 4
E)e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 6| = -b+6
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 6| + |ab - b| = -b+6 + ab - b =ab - 2b + 6
Answer: Option A
Answer: A
Question: A, B and C invested Rs.6500, Rs.1300 and Rs.7800 respectively, in a partnership business. Find the share of B in profit of Rs.11700 after a year?
Options:
A)1300
B)3877
C)1170
D)975
E)7800
Rationale: Explanation:
6500:1300:7800
5:1:6
1/12 * 11700 = 975
Answer:D
Answer: D
Question: 6 mangoes are equal to as many apples as are equal to 4 kiwi. All of them weigh 90kg only. Mango’s weighs are?
Options:
A)6
B)5
C)2
D)7
E)2
Rationale: 6M = xA = 4K
6M + xA + 4K ----- 90 Rs.
6M+6M+6M----- 90 Rs.
18M ------ 90 Rs. => 1M = 5Rs.
Answer: B
Answer: B
Question: The average weight of a class is x pounds. When a new student weighing 100 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
Options:
A)85
B)86
C)88
D)90
E)92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 80 = 6(x-1) --> x = 92 pounds.
Answer: E.
Answer: E
Question: There are 2 white plates, 6 green plates, 8 red plates, 4 pink plates, and 10 purple plates in the cabinet. What is the least number of plates that you have to pull out to make sure that you will have a matching pair? (Assume that all the plates are identical except for the color)
Options:
A)2
B)4
C)12
D)7
E)6
Rationale: Since there are 5 colors, if you take 5 plates, you could still have 1 plate per color and not have a match.
Therefore, upon taking the 6th plate, you will definitely have a match since the 6th plate will form at least a pair with the 1st 5
So 5+1 = 6
Answer is E
Answer: E
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 30 brand B widgets, 30 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
Options:
A)0.02
B)0.095
C)0.03
D)0.0275
E)0.4
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*30 and brand C=0.08*30
Total number of widgets=40+30+30=100
the probability that the widget selected is defective is 0.053=(x*40+0.06*30+0.08*30)/100
=> 40x+1.8+2.4 =5.3
=>40x=1.1
>x=1.1/40=0.0275
Ans D
Answer: D
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number?
Options:
A)54
B)75
C)48
D)46
E)63
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer:C
Answer: C
Question: If two typists can type two pages in two minutes, how many typists will it take to type 22 pages in eleven minutes?
Options:
A)3
B)4
C)6
D)12
E)36
Rationale: In 2 minutes 2 typists type 2 pages which means that in 11 minutes they will type 11 pages but to type 22 pages (2 times) we need 2 times more typists i.e. 2 x 2 = 4 typists.
B
Answer: B
Question: Excluding stoppages, the average speed of a bus is 120 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
Options:
A)15 min
B)18 min
C)16 min
D)20 min
E)40 min
Rationale: In 1hr, the bus covers 120 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (120 - 40) km i.e 80 km at 120 km/hr.
stoppage time = 80/120 hrs
= 40 min
Answer: E
Answer: E
Question: How many figures are required for numbering the pages of a book containing 1000 pages?
Options:
A)2726
B)2878
C)2893
D)2765
E)1811
Rationale: Explanation:
1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 999 = 900 * 3 =2700
1000 = 4
-----------
2893
Answer:C
Answer: C
Question: 18 beavers, working together in a constant pace, can build a dam in 8 hours. How many hours will it take 36 beavers that work at the same pace, to build the same dam?
Options:
A)2.
B)4.
C)5.
D)6
E)8.
Rationale: Total Work = 18*8= 144 Beaver hours
36 Beaver * x =144Beaver hours
x=144/36 = 4
ANSWER:B
Answer: B
Question: A certain city with a population of 72,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
Options:
A)a) 6,000
B)b) 10,800
C)c) 10,900
D)d) 11,000
E)e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 72k
x = 6,000
Answer : A
Answer: A
Question: Excepting B, the rest of the sentences can be the beginners of a paragraph. Excepting in the first answer choice–a, sentence B breaks the sequence of the rest of the choices.
Options:
A)87
B)9
C)917
D)777
E)811
Rationale: Answer:C
Answer: C
Question: A retailer sells pashminas at a ten percent discount. If a pashmina cost him $75 and he wants to make a profit of no less than twenty percent on the cost (after the discount), what is the minimum tag price he needs to put on a pashmina?
Options:
A)90
B)100
C)120
D)140
E)150
Rationale: The minimum tagged price the retailer needs to sell at to make a profit of at least 20%, after offering a 10% discount on tagged price is 1.2*CP(90).
Since, he has to sell the pashmina at 10% discount.
Marked price is 100$
ANS (Option B)
Answer: B
Question: Here 10 programmers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?
Options:
A)16
B)6
C)10
D)60
E)50
Rationale: formulas for it (men1*time1)/work1=(m2*t2)/w2
(10*10)/10=(m2*60)/60
(10*10*60)/(10*60)
ans is 10.
ANSWER:C
Answer: C
Question: A bank lent $250 to a customer for a one-month loan. At the end of the month, the bank received y dollars more than than the amount that was lent due to interest. The bank also charged a service fee $5. In terms of y, what fraction of the amount that the bank received was the service fee?
Options:
A)5/(255+y)
B)5y-1
C)5y/(250-y)
D)5/(250-y)
E)5y-250
Rationale: The amount of money the bank received was (250 + 5+ y) dollars. The $5 service fee as a fraction of the amount received was, therefore, 5/(255+y).
Answer: A.
Answer: A
Question: In what time will Rs.4800 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Options:
A)7
B)7 1/6
C)7 1/3
D)7 1/2
E)8
Rationale: (4800*3*R)/100 = (5000*5*4)/100
R = 7
Answer: A
Answer: A
Question: Find the value(s) of k for which there is no solution for the given set of equations.
2x - ky = -3 and 3x + 2y = 1
Options:
A)4/9
B)2/9
C)2/1
D)4/3
E)2/5
Rationale: 3x + 2y = 1
If there are no set of solutions, then 2−k=322−k=32 or k = −43−43
For k = −43−43, the two lines in the coordinate planes are parallel to each other.
Answer:D
Answer: D
Question: Four people each roll a four die once. Find the probability that at least two people will roll the same number ?
Options:
A)3378
B)27778
C)2211
D)1318
E)2882
Rationale: The number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3
Now total possibilities of rolling a dice = 64
The probability that a no one gets the same number = 6×5×4×364=518
So the probability that at least two people gets same number = 1−518=1318
Answer:D
Answer: D
Question: How many numbers amongst the numbers 6 to 45 are there which are exactly divisible by 15 but not by 10?
Options:
A)Nil
B)1
C)2
D)3
E)More than 3
Rationale: 15,30,45 are divisible by 15.
30 is divisible by 10 also.
So there are 2 numbers exactly divisible by 15 but not by 10
ANSWER:C
Answer: C
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 40%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of P, how much did Lucas pay?
Options:
A)P + 10
B)1.1*P
C)1.12*P
D)0.9*P
E)0.98*P
Rationale: Last year price = P;
This year price = 1.4P;
Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price, thus he paid (1 - 0.3)*1.4P = 0.98P.
Answer: E.
Answer: E
Question: Roy opened a shop investing Rs.20000. Alex joined him 8 months later, investing Rs.34000. They earned a profit of Rs.32000 after completion of two years. What will be Roy's share of profit?
Options:
A)18000
B)19000
C)20000
D)15000
E)17000
Rationale: SoL = ~s- So Roy's share = [15/32] x 32000 = 15000
Answer : D
Answer: D
Question: A group of men decided to do a work in 10days, but 5 of them became absent. If the rest of the group did the work in 12days, Find the original number of men?
Options:
A)15
B)20
C)30
D)25
E)18
Rationale: Original number of men = 5*12 / (12-10) = 30
Answer is C
Answer: C
Question: Martin bought 10 concert tickets, some at the full price of $2.00 per ticket, and some at a discounted price of $1.60 per ticket. If he spent a total of $18.00, how many discounted tickets did he buy?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let x be the number of tickets he bought at $2 per ticket.
then 2 x + (10-x)1.6 = 18
0.4x = 2 => x = 5
discounted tickets = 10 -x = 5
Ans : C
Answer: C
Question: Sum of two consecutive even terms lacks by 98 from their product. Find the sum of these numbers?
Options:
A)22
B)38
C)22
D)98
E)19
Rationale: Explanation:
x(x + 2) â€“ (x + x + 2) = 98
Answer: D
Answer: D
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Options:
A)Rs.21.60
B)Rs.21.68
C)Rs.21.18
D)Rs.21.98
E)Rs.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6
= Rs.21.60
Answer: A
Answer: A
Question: A dealer originally bought 200 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
Options:
A)3q/400
B)3q/2
C)300q
D)q/200
E)300/q
Rationale: The cost of each battery was q/200.
Each battery was sold for 1.5q/200 = 3q/400.
The answer is A.
Answer: A
Question: Jack and Jill are marathon runners. Jack can finish a marathon (41 km) in 4.5 hours and Jill can run a marathon in 4.1 hours.What is the ratio of their average running speed? (Jack: Jill)
Options:
A)41/45
B)15/14
C)4/5
D)5/4
E)Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 41 /(9/2) = 82/9
Average Speed of Jill = 41/(4.1) = 10
Ratio of Average speed of Jack to Jill = (82/9)/10 = 82/90 = 41/45
Answer A
Answer: A
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 150 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?
Options:
A)1289
B)1198
C)281
D)1200
E)282
Rationale: Explanation:
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 150 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 150 = 3k + 150 => 2k = 300=> k = 150
The initial quantity of water in A = 8k = 8 * 150= 1200 liters.
Answer: Option D
Answer: D
Question: If the speed of X meters per minute is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)
Options:
A)0.06
B)0.6
C)6
D)0.03
E)0.3
Rationale: X meters per second -->
--> 60X meter per hour(as there are 60 minute in one hour);
--> 60X/1,000=kilometers per hour (as there are 1,000 meters in one kilometer).
Answer: A.
Answer: A
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Options:
A)6000
B)6200
C)6400
D)6600
E)6650
Rationale: Number of bricks = Volume of the wall/Volume of 1 brick
= (800 x 600 x 22.5/25 x 11.25 x 6) = 6400.
ANSWER C
Answer: C
Question: A milk vendor sells milk at Cost Price but still gains 20%. Find the ratio of milk and water in every gallon that he sells.
Options:
A)4:1
B)5:1
C)5:2
D)6:1
E)None of these
Rationale: Let the vendor buy 100 L of milk. For him to make 20% profit, he has to turn this 100 L into 120 L without incurring any cost. So he has to mix 20 L of water. So ratio of milk to water is 100/20=5 ;ANSWER:B
Answer: B
Question: If x is the product of the positive integers from 1 to 9, inclusive, and if i, k, m, and p are positive integers such that x=2i3k5m7px=2i3k5m7p, then i + k + m + p =
Options:
A)4
B)7
C)8
D)11
E)13
Rationale: x= 9!
= 9* 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= (3^2) * (2^3) * 7 * (2*3) * 5 * 2^2 * 3 * 2 * 1
= 2^7 * 3^4 * 5 * 7
= 2^i * 3^k * 5^m * 7^p
i+k+m+p = 7+4+1+1
= 13
Answer E
Answer: E
Question: A trained covered x km at 30 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)22.5
B)99
C)24
D)66
E)887
Rationale: Total time taken = x/30 + 2x/20 hours
= 2x/15 hours
Average speed = 3x/(2x/15) = 22.5 kmph
Answer: A
Answer: A
Question: If x, y, and z are positive integers and 3x = 4y = 7z, then the least possible value of x - y + z is
Options:
A)33
B)40
C)49
D)19
E)61
Rationale: x - y + z = - 3x/4 + x + 3x/7
= (- 21 + 28 + 12 )x/28 = 19x/28
19 is not divisible by 28(it's a prime #), so for least value, x = 28
Answer - D
Answer: D
Question: Find the value of m 12519 x 9999 = m?
Options:
A)125177481
B)353654655
C)545463251
D)725117481
E)477899932
Rationale: 12519 x 9999 = 12519 x (10000 - 1)
= 12519 x 10000 - 12519 x 1
= 125190000 - 12519
= 125177481
A
Answer: A
Question: If 10 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Options:
A)80
B)63
C)120
D)160
E)1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 10c2
for vertical 8c2
total parallelogram is 10 c2*8c2=45*28
=1260
ANSWER:E
Answer: E
Question: Today is Thursday. The day after 55 days will be?
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)wednesday
Rationale: Explanation:
55 days = 7 weeks 6 days = 6 odd days
Hence if today is Thursday, After 55 days, it will be = (Thursday + 6 odd days)
= Wednesday
Answer: Option E
Answer: E
Question: A father divides his estate among his three sons, in such a manner, that:
The first has $1000 less than half of the whole;
The second has 800 less than one third of the whole;
The third has 600 less than one fourth of the whole;
What is the value of the estate?
Options:
A)18800
B)28800
C)38800
D)48800
E)None
Rationale: Solution
If the whole estate be represented by x, then the several shares will be x/2 - 1000, and x/3 - 800, and x/4 - 600.
And as these constitute the whole estate, they are together equal to x.
We have then this equation x/2 - 1000 + x/3 - 800 + x/4 - 600 = x.
Which reduced gives x = 28800
Proof 28800/2 - 1000 + 28800/3 - 800 + 28800/4 - 600 = 28800
Answer B
Answer: B
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph.
B)17 kmph.
C)18 kmph.
D)11 kmph.
E)12 kmph.
Rationale: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2
= 10 kmph.
Answer:A
Answer: A
Question: The unit digit in the product (224 * 607 * 214 * 863) is:
Options:
A)2
B)5
C)6
D)8
E)10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*7*4*3) = 6
ANSWER: C
Answer: C
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 weavers in 16 days?
Options:
A)16
B)32
C)64
D)96
E)128
Rationale: 1 weaver can weave 1 mat in 4 days.
16 weavers can weave 16 mats in 4 days.
16 weavers can weave 64 mats in 16 days.
The answer is C.
Answer: C
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 12?
Options:
A)A)100
B)B)120
C)C)250
D)D)200
E)E)160
Rationale: Then, 10% of x= 12
(10/100)x = 12
x = (12*100*)/10= 120
Answer is B
Answer: B
Question: The Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women?
Options:
A)14/33
B)7/33
C)2/7
D)13/73
E)12/27
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792.
To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6.
And, select 3 women from 8 = 8C3 = 56.
3 women and 2 men = (6)(56) = 336
Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33
Answer: A
Answer: A
Question: The inverse ratio of 3: 2: 1 is?
Options:
A)2:9:5
B)2:3:0
C)2:3:5
D)2:3:6
E)2:3:1
Rationale: 1/3: 1/2: 1/1 = 2:3:6
Answer:D
Answer: D
Question: Compute the value of a + b + c + d.
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let s = a + b + c + d. Subtracting s from each side of the equations gives us
ab - a - b = 13-s
bc - b - c = 27- s
cd - c -d = 30 - s
da - d - a = 17 - s
Adding one to each side of the equations and applying Simon's Favorite Factoring Trick gives
us
(a - 1)(b - 1) = 14 - s
(b - 1)(c - 1) = 28 -s
(c - 1)(d - 1) = 31 - s
(d - 1)(a - 1) = 18 - s
Multiplying the first and third equations and the second and fourth equations allows us to write
the following equality:
(a - 1)(b - 1)(c - 1)(d - 1) = (14 - s)(31 - s) = (28 - s)(18 - s)
Expanding and solving for s gives us s = 70 .
correct answer D
Answer: D