divelab/Sys2Bench huggingface dataset:
Question: If x > 1, which of the following decreases as x decreases?
I.1/( x + x^2)
II. 1/(2x^2 − x)
III. (x + 1)
Options:
A)I only
B)II only
C)III only
D)I and II only
E)II and III only
Rationale: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 1/20
x=3-> 3+9 = 1/12 ...increased
ST2:x= 4-> 2*16-4 =1/ 28
x=3->2*9-3 = 1/15
Increased
St3: x=4-> 5
x=3->4
Ans: C
Answer: C
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer Q between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
Options:
A)Q=12
B)Q=15
C)Q=17
D)Q.18
E)Q=20
Rationale: Since we are concerned with integers between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Answer: D
Question: A man sells a horse for Rs.620 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)227
B)299
C)740
D)860
E)771
Rationale: CP = SP + 1CP = SP - g
620 + x = 980 - 2x
3x = 360 => x = 120
CP = 620+ 120= 740
Answer: C
Answer: C
Question: Logan buys 100 shares of par value Rs. 30 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
Options:
A)2
B)4
C)5
D)36
E)8
Rationale: Face value of each share = Rs.30
Total dividend received by Logan = 100Ã—30Ã—12/100 = Rs.360
Let market value of 100 shares = Rs.x
xÃ—10/100=360
x = 3600
ie, Market value of 100 shares = Rs.3600
Hence, Market value of each share = Rs.36
Answer is D.
Answer: D
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 1/7 %
B)33 8/3 %
C)33 1/3 %
D)33 1/8 %
E)37 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer: C
Answer: C
Question: In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
Options:
A)1 hr
B)2 hr
C)1.5 hr
D)2.5 hr
E)3 hr
Rationale: Explanation :
Ratio of speeds = 3:4Distance remaining constant, the ratio of time taken = 4:3A takes 0.5 hours more than BHence time taken by A=4×0.5= 2 hour
Answer : B
Answer: B
Question: From the sale of sleeping bags, a retailer made a gross profit of 15% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
Options:
A)3.0
B)3.36
C)24.34
D)25.0
E)31.36
Rationale: Cost price * 1.15 = Selling price --> Cost price * 1.15 = $28 --> Cost price = $24.34.
Answer: C.
Answer: C
Question: A wildlife preserve is being planned for 4,000 rhinoceroses. The preserve is to contain a total of 10,000 acres of watering area, plus 100 acres of grazing area for each rhinoceros. If the number of rhinoceroses is expected to increase by 10 percent, how many thousand acres should the preserve have in order to provide for the increased population?
Options:
A) 450
B) 330
C) 320
D) 310
E) 300
Rationale: Number of rhinos = 4000
Watering area = 10,000 acres
Number of rhino to increase by 10 percent ,then number of rhino = 4400
Grazing area for a rhino = 100
Total grazing area for 4400 rhinos= 4400 * 100 = 4,40,000
Total area required for the wildlife preserve = 4,40,000 + 10,000 = 4,50,000 = 450 * 1000
Answer A
Answer: A
Question: How many cubes of 10cm edge can be put in a cubical box of 1m edge
Options:
A)3348
B)2888
C)1000
D)2877
E)3778
Rationale: Explanation:
number of cubes=(100x100x100)/(10x10x10)=1000
Answer: C) 1000
Answer: C
Question: In a group of 26 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
Options:
A)7
B)6
C)5
D)4
E)8
Rationale: C
5
Add 7 + 10 + 4 to get 21.
Then subtract 21 from the total students ⇒ 26 – 21 = 5.
Answer is C
Answer: C
Question: If 9a - b = 10b + 65 = -12b - 2a, what is the value of 11a + 11b?
Options:
A)-11
B)-5
C)0
D)5
E)11
Rationale: (i) 9a - 11b = 65
(ii) 2a + 22b = -65
Adding (i) and (ii):
11a + 11b = 0
The answer is C.
Answer: C
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)15 hours
B)18 hours
C)20 hours
D)25 hours
E)35 hours
Rationale: Let A fill tank in x hrs.
Therefore tank filled in one hrs is 1/x.
And B pipe is twice than A means 2 (1/x).
C pipe is twice than B means 2 (2 (1/x) ) i.e 4/x.
1/x+2/x+4/x = 1/5.
7/x = 1/5.
x = 35 hrs.
ANSWER :e
Answer: E
Question: 17 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)154
B)184
C)240
D)272
E)306
Rationale: 2*17C2 = 2*136 = 272
The answer is D.
Answer: D
Question: A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:
Options:
A)8.5 min
B)7.5 min
C)1.5 min
D)9.5 min
E)4.5 min
Rationale: Explanation:
B runs around the track in 10 min.
i.e , Speed of B = 10 min per round
A beats B by 1 round
Time taken by A to complete 4 rounds
= Time taken by B to complete 3 rounds
= 30 min
A's speed = 30/4 min per round
= 7.5 min per round
Hence, if the race is only of one round A's time over the course = 7 min 30 sec
Answer: B
Answer: B
Question: A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph of 3 edges and 3 points. The degree of a point is the number of edges connected to it. For, example, a triangle is a graph with 3 points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any through sequence of edges. The number of edges 'e' in the graph must satisfy the condition
Options:
A)11 ≤ e ≤ 66
B)10 ≤ e ≤ 66
C)11 ≤ e ≤ 65
D)0 ≤ e ≤ 11
E)None of these
Rationale: Explanation :
The least number of edges will be when one point is connected to each of the other 11 points, giving a total of 11 lines. One can move from any point to any other point via the common point.
The maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.
Answer : A
Answer: A
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 2 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
Options:
A)2y
B)4y
C)5y
D)6y
E)13y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-2)=12 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/12
Solving we get, x=13y
Now Anthony's Advance is x=13y .So answer should be E.
Answer: E
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 350-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
Options:
A)1,108
B)2,900
C)2,108
D)2,124
E)2,256
Rationale: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 350 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 350x8 = 2800 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 2900 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 2900 (ANSWER B)
Answer: B
Question: A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?
Options:
A)15
B)14
C)12
D)10
E)11
Rationale: Explanation :
There are two equations to be formed 40m + 50f = 1000.
250m + 300f + 40 x 15m + 50 x 10f = A.
850m + 8000f = A.
m and f are the number of males and females. A is the amount paid by the employer.
Then the possible value of f = 8,9,10,11,12.
Iif f= 8, M =15.
If f = 9,10,11 then m will not be an integer while f =12 then m will be 10.
By putting f = 8 and m=15 , A = 18800.
when f =12 and m= 10 then A = 18100.
Hence, the number of males is 10.
Answer : D
Answer: D
Question: A batsman makes a score of 100 runs in the 17th inning and thus increases his averages by 5. What is his average after 17th inning?
Options:
A)39
B)35
C)20
D)40.5
E)41.5
Rationale: let the average after 16th inning =x
then total run after 16th inning=16x
then total run after 17th inning=16x+100
then average run after 17th inning=(16x+100)/17
(16x+100)/17=x+5 = > 16x+100 = 17x+85 => x =15
x=15;
average after 17th inning =15+5=20
ANSWER:C
Answer: C
Question: The average age of a husband, wife and their child 12 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)19.01 years
B)5.25 years
C)16 years
D)15 years
E)4.75 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/12
= 4.75 years.
Answer:E
Answer: E
Question: Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 2107 miles?
Options:
A)Two hours and 30 minutes.
B)One hour and 10 minutes.
C)Two hours and 25 minutes.
D)Three hours and 5 minutes.
E)Four hours and 20 minutes.
Rationale: Answer is D. Three hours and 5 minutes.
Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)
So time before collision is total distance / total speed = 2107/602 = 3 hours and 5 mins
Answer: D
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Options:
A)1/5
B)2/47
C)3/8
D)12/455
E)1/28
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (Â²Câ‚)(â´Câ‚‚)/Â¹âµCâ‚ƒ
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455.
D
Answer: D
Question: If the difference between compound interest(interest compounded yearly) and simple interest on a sum for 3 years at 20% p.a. is Rs.132, then the sum is
Options:
A)Rs.3500
B)Rs.1500
C)Rs.2500
D)Rs.3000
E)None
Rationale: C.I-S.I=132
C.I=A-P
A=P(1+(R/100))^n
A=x(1+(20/100))^3
A=x(6/5)^3
A=216/125(x)
C.I=(91/125)x
S.I=(PNR)/100=(x*3*20)/100=(6/10)x
diff=132
diff=(91/25)x-(6/10)x=(182x-150x)/250=32x/250
32x/250=132
x=(132*250)/32
x=1031.25
ANSWER:E
Answer: E
Question: The product of the prime numbers between 0 and 20 is closest to...
Options:
A)10^5
B)10^6
C)10^7
D)10^8
E)10^9
Rationale: Write out the primes 1 - 20
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19
Round the numbers off in multiples of 5. Try to alternate rounding up and down
5 x 5 x 5 x 5 x 10 x 10 x 20 x 20
25 x 25 x 10 x 10 x 20 x 20
pull out 10 from each number
10^6 (2.5 x 2.5 x 2 x 2)
10^6 (5 x 4)
10^7 (2)
round off the 2.
answer is C
Answer: C
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
Options:
A)22
B)16
C)27
D)187
E)11
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2
=> 2a = 32 => a = 16.
Answer:B
Answer: B
Question: A single discount equivalent to the discount series of 25%, 10% and 5% is?
Options:
A)31.5
B)31.8
C)31.6
D)31.3
E)35.9
Rationale: 100*(75/100)*(90/100)*(95/100)
= 64.1
100 - 64.1 = 35.9
Answer:E
Answer: E
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $900. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 10% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
Options:
A)$100
B)b $115
C)c $187.5
D)d $130.5
E)e $135.5
Rationale: Purchase cost = 900/1500= $ 0.6
25% above the cost per head = (125/100)*0.6= $ 0.75
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.75 = $ 750
Remaining were sold at a price equal to 10% less than the price each head sold for on the day before i.e , (90/100)*0.75 = $ 0.675
Hence selling cost for the remaining cabbage = 500 * 0.675 = $ 337.5
Total selling cost = 750 + 337.5 = $ 1087.5
Gross profit = $ 1087.5 - $ 900 = $ 187.5
Hence Answer is C.
Answer: C
Question: Anil invested a capital of Rs.5000 and Sunil invested Rs.10000. Anil invested for a time period which is double than the time period for which Sushil invested. How will a profit of Rs.4000 be divided between them?
Options:
A)1000, 3000
B)3000,1000
C)2500,1500
D)2000,2000
E)3000,2000
Rationale: suppose time duration for sunil is 'x' and thus time duration for anil will be '2x'
So their investment ratio will be 5000*2x:10000*x= 1:1
Therefore profit 4000 will be divided into 1:1 ratio i.e. 2000 & 2000
ANSWER:D
Answer: D
Question: A train passes a station platform in 32 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
Options:
A)340
B)360
C)380
D)400
E)420
Rationale: The speed of the train is 72 * 5/18 m/s = 20 m/s
The length of the train is 20 x 12 = 240 m
platform + 240 = 20 * 32
platform = 640 - 240 = 400
The answer is D.
Answer: D
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 5 days?
Options:
A)5/18
B)1/6
C)1/4
D)1/9
E)2/6
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 5 days = 5 (1/18) = 5/18.
ANSWER A
Answer: A
Question: In store A there are 20 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
Options:
A)3:16.
B)2:3.
C)1:3.
D)3:4.
E)2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
20x : 40x
X:2X
Price :
4y:3y
Total revenue
4xy : 6xy
2:3
Answer is B
Answer: B
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 15 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)78
B)60
C)26
D)23
E)12
Rationale: Relative speed = 45 + 15 = 60 km/hr.
60 * 5/18 =50/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/50 = 60 sec.
Answer:B
Answer: B
Question: The cost of an item was reduced from its usual selling price of $23.99 to $17.99. Which of the following is closest to the percent decrease in the price of the item?
Options:
A)17%
B)21%
C)24%
D)25%
E)42%
Rationale: The price decreased by 23.99 - 17.99 = $6.
$6 is a bit more than 25% of original price of $24.
Answer: D.
Answer: D
Question: In a bag,there are coins of 25 p,10 p and 5 p in the ratio of 1 : 2 : 3.If there are Rs.30 in all,how many 5 p coins are there ?
Options:
A)50
B)100
C)150
D)200
E)250
Rationale: Solution
Let the number of 25 p,10 p and 5 p coins be x,2x and 3x respectively.
Then,sum of their values = Rs.(250x/100 +10x2x100 +5x3x/100) = Rs.60x/100
∴60/100 = 30 x =30x100/60 = 50.
Hence,the number of 5 p coins = (3x50) = 150
Answer C
Answer: C
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 5% chemical X and 95% chemical Y, then what percentage of the resulting mixture is chemical X?
Options:
A)24%
B)26%
C)28%
D)30%
E)32%
Rationale: The amount of chemical X in the solution is 20 +0.05(80) = 24 liters.
24 liters / 100 liters = 24%
The answer is A.
Answer: A
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.575 in all. Find the share of B?
Options:
A)130
B)120
C)218
D)140
E)145
Rationale: A+B+C = 575
A = 3B
3B+B+B-25 = 575
5B = 600
B = 120
Answer: B
Answer: B
Question: How many liters of water must be added to 18 liters of milk and water containing 10% water to make it 40% water?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: By rule of alligation:
40% - 10% = 30%
100% - 40% = 60%
Quantity of pure water : Quantity of the mixture = 1 : 2
There are 18 liters of mixture, so we need to add 9 liters of pure water.
The answer is D.
Answer: D
Question: In Kiran's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Kiran and he thinks that Kiran's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Kiran?
Options:
A)70 kg
B)69 kg
C)61 kg
D)67 kg
E)65 kg
Rationale: Explanation:
Let Kiran's weight = x. Then
According to Kiran, 65 < x < 72 ----(equation 1)
According to brother, 60 < x < 70 ----(equation 2)
According to mother, x ≤≤ 68 ----(equation 3)
Given that equation 1,equation 2 and equation 3 are correct. By combining these equations, we can write as
65<x≤68
i.e., x = 66 or 67 or 68
Average of different probable weights of Kiran = 66+67+683=67
Answer: Option D
Answer: D
Question: The average of six numbers is 3.75. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
Options:
A)4.7
B)4.6
C)4.0
D)4.1
E)4.9
Rationale: Explanation:
Sum of the remaining two numbers = (3.75 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 22.50 - (6.8 + 7.7) = 22.50 - 14.5 = 8.
Required average = (8 / 2) = .
Answer: C) 4.0
Answer: C
Question: A committee of 5 persons is to be formed from 3 company secretaries, 4 economists and 1 chartered accountant. What is the probability that each of the three professions is represented in the committee?
Options:
A)1/28
B)3/28
C)60/14
D)4/28
E)3/14
Rationale: 3/8*4/7*1/6*5! = 3/14. We are multiplying by 5! because we can choose secretary,economist, and accountant is several way:
Answer: C.
Answer: C
Question: A batsman scored 100 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45(4/11) %
B)40 %
C)45(5/11) %
D)44(5/11) %
E)None of these
Rationale: Explanation :
Total runs scored = 100
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 100 - 60 = 40
Required % = (40/100) × 100 = 40%
Answer : Option B
Answer: B
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 10:30 am. They shall first cross each other at ?
Options:
A)7:15 am
B)7:30 am
C)10: 42 am
D)7:50 am
E)7:60 am
Rationale: Explanation:
Relative speed between two = 6-1 = 5 round per hour
They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.
So 10:30 + 12 mins = 10:42
Option C
Answer: C
Question: Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?
Options:
A)$10
B)$20
C)$30
D)$40
E)$50
Rationale: 2 × (10 + 5) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars
correct answer is C)$30
Answer: C
Question: If x = 3d, where d is a prime number greater than 2, how many different positive even divisors does x have, including x?
Options:
A)0
B)1
C)2
D)3
E)It cannot be determined from the information given
Rationale: d is prime greater than 2 thus d is odd
3d is odd
Thus no even factors
Ans:A
Answer: A
Question: Elizabeth can get a certain job done in 15 days, and Tony can finish only 75% of that job within the same time. Tony worked alone for several days and then Elizabeth joined him, so they finished the rest of the job in 6 days, working together.
For how many days have each of them worked and what percentage of the job have each of them completed?
Options:
A)5 days and 40%
B)6 days and 30%
C)6 days and 40%
D)7 days and 40%
E)7 days and 30%
Rationale: First we will find the daily productivity of every worker. If we consider the whole job as unit (1), Elizabeth does 115 of the job per day and Tony does 75% of 115, i.e.
75100⋅115=120. Suppose that Tony worked alone for x days. Then he finished x20 of the total job alone. Working together for 6 days, the two workers finished 6⋅(115+120)=6⋅760=710 of the job.
The sum of x20 and 710 gives us the whole job, i.e. 1. So we get the equation:
x20+710=1
x20=310
x=6. Tony worked for 6 + 6 = 12 days and Elizabeth worked for 6 days. The part of job done is 12⋅120=60100=60% for Tony, and 6⋅115=40100=40% for Elizabeth.
Answer is C.
Answer: C
Question: How many different positive integers are factors of 36 ?
Options:
A) 4
B) 6
C) 7
D) 9
E) 11
Rationale: 6×6=3^2 × 2^2
So total factors = (2+1)(2+1) = 9
Answer: D
Answer: D
Question: What is the maximum number of pieces that a circular pizza can be cut into with 6 linear cuts?
Options:
A)12
B)13
C)16
D)20
E)22
Rationale: 1 cut makes 2 pieces
a second cut can make 4 pieces by cutting through 2 of the pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
a fifth cut can make 16 pieces by cutting through 5 of the pieces
a sixth cut can make 22 pieces by cutting through 6 of the pieces
E
Answer: E
Question: A departmental store charges the commission of 18 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
Options:
A) $215,000
B) $365,000
C) $115,000
D) $200,000
E) $160,000
Rationale: 24,000 = 0.18 *(50000) + 0.10 (x - 50000)
24000 - 9000 = 0.10 (x-50000)
150000 = x - 50000
x = 2,00,000
Answer : D
Answer: D
Question: Five times a number equals one hundred. The number is
Options:
A)50
B)10
C)15
D)25
E)20
Rationale: Since five times the number equals one hundred, then the number equals one hundred divided
by five. Therefore the number is 100/ 5 = 20.
correct answer E
Answer: E