divelab/Sys2Bench huggingface dataset:
Question: For any number z, z* is defined as the greatest positive even integer less than or equal to z. What is the value of 5.2 – 5.2*?
Options:
A)0.2
B)1.2
C)1.8
D)2.2
E)4.0
Rationale: Since z* is defined as the greatest positive even integer less than or equal to z, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).
Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2
Answer: B.
Answer: B
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $40. What is the percent decrease?
Options:
A)20%
B)30%
C)40%
D)70%
E)60%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 40 = 60. The “original” is our starting point; in this case, it’s 100. (60/100)*100 = (0.6)*100 = 60%.
E
Answer: E
Question: Increasing the original price of a certain item by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by what percent?
Options:
A)31.25
B)37.5
C)50.0
D)52.5
E)44.0
Rationale: We're told that the original price of an item is increased by 20% and then THAT price is increased by 20%....
IF....
Starting value = $100
+ 20% = 100 + .20(100) = 120
+ 20% = 120 + .20(120) = 120 + 24 = 144
The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:
Percentage Change = (New - Old)/Old = Difference/Original
Doing either calculation will yield the same result:
44/100 = 44%
Final Answer:
E
Answer: E
Question: The average age of a group of persons going for picnic is years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
Options:
A)5
B)10
C)20
D)40
E)50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 20 x 15 = 15.5(x+20)
= 0.5x = 10
x = 20.
Answer C
Answer: C
Question: X starts a business with Rs.45000. Y joins in the business after 4 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
Options:
A)1:2
B)2:1
C)1:3
D)3:1
E)9:4
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—8
=45Ã—12:30Ã—8
=3Ã—12:2Ã—8
=9:4
Answer: Option E
Answer: E
Question: There are 80 coins, among them one coin weighs less compared to other. You are given a physical balance to weigh. In how many weighing the odd coin can be found.
Options:
A)3
B)5
C)6
D)7
E)4
Rationale: 80 divide as
27 27 26
9 9 9
3 3 3
1 1 1
so weighings are 4
ANSWER:E
Answer: E
Question: What is the compound interest paid on a sum of Rs.3000 for the period of 2 years at 10% per annum.
Options:
A)630
B)620
C)610
D)600
E)None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Total % of interest= 10 + 11=21
Total interest = 21 % 3000= 3000 * (21/100)= 630
Answer A
Answer: A
Question: A pair of articles was bought for $50 at a discount of 50%. What must be the marked price of each of the article?
Options:
A)$25
B)$12.50
C)$29.65
D)$35.95
E)$45.62
Rationale: S.P. of each of the article = 50/2 = $25
Let M.P = $x
50% of x = 25
x = 25*.5 =$12.50
Answer is B
Answer: B
Question: The G.C.D. of 1.08, 0.36 and 0.9 is?
Options:
A)0.03
B)0.9
C)0.18
D)0.108
E)none of these
Rationale: Given numbers are 1.08,0.36 and 0.90.
H.C.F of 108, 36 and 90 is 18
H.C.F of given numbers=0.18.
Correct Options:C
Answer: C
Question: A certain no. when divided by 35leaves a remainder 25, what is the remainder if the same no.be divided by 15?
Options:
A)3
B)4
C)6
D)8
E)9
Rationale: Explanation:
35 + 25 = 60/15 = 4 (Remainder)
B
Answer: B
Question: x^2 + qx + 72 = 0 has two distinct integer roots; how many values are possible for q?
Options:
A)3
B)6
C)8
D)12
E)24
Rationale: For a quadratic equation ax^2+qx+c=0, we know that -q/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + qx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: D
Question: A number consists of 3 digit whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:
Options:
A)22
B)24
C)77
D)26
E)81
Rationale: Explanation:
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
Answer: B
Answer: B
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
Options:
A)10 min
B)20 min
C)25 min
D)30 min
E)40 min
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Answer: A
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $35.19. How much did the meal cost without the tip?
Options:
A)$28.98
B)$29.91
C)$30.15
D)$30.60
E)$30.85
Rationale: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $35.19:
1.15x = 35.19
Divide both sides by 1.15:=>x=35.19/1.15=30.60
correct answer D)$30.60
Answer: D
Question: A rocket soars for 12 seconds at 150 meters per second. It then plummets 600 meters in 3 seconds. What is the average speed of the rocket in meters per second?
Options:
A)140
B)150
C)155
D)160
E)175
Rationale: When soaring, the rocket travels a total distance of 1800m(150m/s for 12s)
While plummeting the rockets travel distance of 600m in 3s
The total distance traveled is 2400m(1800 + 600)
The time taken to travel this distance is 15s(12 + 3)
Average speed = 2400/15 = 160
ANS: (Option D)
Answer: D
Question: 12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
Options:
A)360
B)384
C)432
D)470
E)480
Rationale: First of all, I think the question means that "the chairs numbered 1 AND 8 should be occupied".
So, we have that the chairs numbered 1 AND 8 should be occupied and no two adjacent chairs must be occupied. Notice that chairs #2, 7, and 9 cannot be occupied by any of the men (because no two adjacent chairs must be occupied.).
1-2-3-4-5-6-7-8-9-10-11-12
If the third man occupy chair #3, then the fourth man has 5 options: 5, 6, 10, 11, or 12;
If the third man occupy chair #4, then the fourth man has 4 options: 6, 10, 11, or 12;
If the third man occupy chair #5, then the fourth man has 3 options: 10, 11, or 12;
If the third man occupy chair #6, then the fourth man has 3 options: 10, 11, or 12;
If the third man occupy chair #10, then the fourth man has 1 options: 12.
Total of 5+4+3+3+1=16 cases. For each case the 4 men can be arranged in 4! ways, thus the total number of arrangements is 16*4!=384.
Answer: B.
Answer: B
Question: How many ways someone can make with 8 shirts and 6 pants?
Options:
A)50
B)45
C)55
D)52
E)48
Rationale: If you can only wear one shirt and one pair of pants, then you can make 8*6 = 48 combinations.
Answer:E
Answer: E
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes K, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
Options:
A) 6
B) 9
C) 10
D) 12
E) 15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, K=15-5 = 10.C
Answer: C
Question: a 50 is divided in two parts in such a way its reciprocal is 1/12.find the no?
Options:
A)20,30
B)20,40
C)20,10
D)30,10
E)30,40
Rationale: 1/x + 1/(50-x) = 1/12
=> (x^2-50x+600) = 0
=> (x-20)(x-30) = 0
=> x = 20,30
numbers are 20,30.
ANSWER:A
Answer: A
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. An ellipse has a center at (0, 0) and minor/major axes lengths of 1, 4, respectively. Some points, such as the center (0, 0), are inside the ellipse, but a point such as (0, 2) is on the ellipse but not in the ellipse. How many lattice points are in the ellipse?
Options:
A)26
B)23
C)5
D)4
E)7
Rationale: The lattice points that are in the ellipse, that lie on the x axes, are (0, 0), (0, 1), (0, 2), (0, 3), (0, -1), (0, -2), and (0, -3). There are no other points in the ellipse. The only point on y axis in the ellipse is the center which we counted already.
There are a total of 7 lattice points in the circle.
Answer: E
Answer: E
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
Options:
A)4x + 6y
B)x + y + 4
C)4x - 9y
D)9x + 4y
E)x + y - 4
Rationale: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
correct answer C
Answer: C
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (10,4), which of the following coordinates would most likely be A's?
Options:
A)(17, -2)
B)(10, 6)
C)(6, 8)
D)(-10, 3)
E)(-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10.
B rules..
Answer: B
Question: A man buys an article and sells it at a profit of 10%. If he had bought it at 10% less and sold it for Rs.55 less, he could have gained 15%. What is the cost price?
Options:
A)197
B)375
C)846
D)278
E)268
Rationale: CP1 = 100 SP1 = 110
CP2 = 90 SP2 = 90 * (115/100) = 103.5
6.5 ----- 100
55 ----- ? => 846
Answer:C
Answer: C
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. 3000 more than D, what is B's share?
Options:
A)A)8239
B)B)2900
C)C)6000
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 = 3000 => x = 3000.
B's share = Rs. 2x = 2 * 3000 = Rs. 6000.
Answer: C
Answer: C
Question: If 1/8 of a pencil is black ½ of the remaining is white and the remaining 3 ½ is blue find the total length of the pencil?
Options:
A)9
B)5
C)7
D)8
E)4
Rationale: Let the total length be xm
Then black part =x/8cm
The remaining part=(x-x/8)cm=7x/8cm
White part=(1/2 *7x/8)=7x/16 cm
Remaining part=(7x/8-7x/16)=7x/16cm
7x/16=7/2
x=8cm
Answer is D.
Answer: D
Question: The volume of a cube is 3375 cc. Find its surface.
Options:
A)1350
B)1150
C)1456
D)1254
E)1489
Rationale: a3 = 3375 => a = 156a2 = 6 * 15 * 15 = 1350Answer: A
Answer: A
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.5
B)1.8
C)1.2
D)1.1
E)1.9
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:A
Answer: A
Question: (1/3) of a number is 5 more than the (1/6) of the same number? find the no.
Options:
A)6
B)36
C)30
D)72
E)62
Rationale: x/3=5+x/6
x/3-x/6=5
x/6=5
x=30
ANSWER:C
Answer: C
Question: The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:
Options:
A)10
B)11
C)55
D)110
E)330
Rationale: 377,910 = 3 * 3 * 10 * 4199
3,310 = 3 * 10 *10 * 11
So, x must have 10 and 11 as factors.
--> Least value of x is 110.
Answer:D
Answer: D
Question: Using all the letters of the word "BETA", how many words can be formed, which begin with B and end with A?
Options:
A)5
B)6
C)8
D)9
E)2
Rationale: There are five letters in the given word.
Consider 4 blanks ....
The first blank and last blank must be filled with B and A all the remaining three blanks can be filled with the remaining 2 letters in 2! ways.
The number of words = 2! = 2.
Answer: E
Answer: E
Question: A wheel of a car of radius 21 cms is rotating at 400 RPM. What is the speed of the car in km/hr?
Options:
A)79.2 km/hr
B)47.52 km/hr
C)7.92 km/hr
D)31.68 km/hr
E)3.96 km/hr
Rationale: Explanatory Answer
The radius of the wheel measures 21 cm.
In one rotation, the wheel will cover a distance which is equal to the circumference of the wheel.
∴ in one rotation this wheel will cover 2 * π * 21 = 132 cm.
In a minute, the distance covered by the wheel = circumference of the wheel * rpm
∴ this wheel will cover a distance of 132 * 400 = 52800 cm in a minute.
In an hour, the wheel will cover a distance of 52600 * 60 = 3168000 cm.
Therefore, the speed of the car = 3168000 cm/hr = 31.68 km/hr
Choice D is the correct answer.
Answer: D
Question: If 2.5 of a number is equal to 0.75 of another number, the ratio of the numbers is :
Options:
A)2 :3
B)3 :4
C)3:10
D)20 : 3
E)30:7
Rationale: 2.5A = 0.75B
-> A/B = 0.75/2.5 = 75/250 = 3/10
:. A : B = 3 : 10
ANSWER:C
Answer: C
Question: One-third of 600 is what percent of 120 ?
Options:
A)313.2
B)30.1
C)12.24
D)None of these
E)166.6
Rationale: Answer
Let one-third of 600 is N% of 120.
∵ 600/3 = (N x 120)/100
∴ N = (200x 100) / 120 = 166.6
Correct Option: E
Answer: E
Question: If 15 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?
Options:
A)127
B)240
C)287
D)450
E)281
Rationale: Explanation:
Let the required no of hectares be x. Then
Men --- Hectares---Days
15---------80---------24
36---------x---------30
More men, More hectares (Direct proportion)
More days, More hectares (Direct proportion)
x=36/15*30/24*80
x= 240
Answer: B
Answer: B
Question: A train running at the speed of 108 km/hr crosses a pole in 7 seconds. Find the length of the train.
Options:
A)150 meter
B)145 meter
C)140 meter
D)135 meter
E)210 meter
Rationale: Explanation:
Speed = 108*(5/18) m/sec = 30 m/sec
Length of Train(Distance) = Speed * Time
=30*7=210 meter
Option E
Answer: E
Question: A case contains c cartons. Each carton contains b boxes, and each box contains 600 paper clips. How many paper clips are contained in 2 cases?
Options:
A)600bc
B)600b/c
C)1200bc
D)1200b/c
E)1200/bc
Rationale: 2 cases * c cartons/case * b boxes/carton * 600 clips/box = 1200bc paper clips
The answer is C.
Answer: C
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
Options:
A)1/13
B)3/13
C)1/4
D)9/52
E)8/52
Rationale: there are only 4 jack in 52 cards so selecting 1 is done in 4c1=4
4 queens selecting 1 is done in 4c1=4
4 kings selecting 1 is done in 4c1=4
total selecting 1 card from 52 cards is 52c1
4+4+4/52
12/52
3/13
ANSWER:B
Answer: B
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 3 days at a time. If A starts they finish the task in exactly 9 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
Options:
A)8
B)6
C)4
D)5
E)9/2
Rationale: Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 6No. of days when B works = 3 → 6x + 3y = 1
When B starts:
No. of days when A works = 4 No. of days when A works = 5 → 5x + 4y = 1
Solving the above two equations for xy
x = 1/9 y = 1/9
→ Total work done by AB in a day = 1/9 + 1/9 = 2/9
→ No. of days to complete the work when both work together = 9/2;
Answer: E
Answer: E
Question: Suraj has a certain average of runs for 14 innings. In the 15th innings he scores 140 runs thereby increasing his average by 8 runs. What is his average after the 15th innings?
Options:
A)48
B)28
C)36
D)72
E)27
Rationale: To improve his average by 8 runs per innings he has to contribute 14 x 8 = 112 runs for the previous 14 innings.
Thus, the average after the 15th innings
= 140 - 112 = 28.
ANSWER:B
Answer: B
Question: Total natural no. from 11 to 90 which is divisible 7.
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: these no. are 14,21,28,35,...,84.
these are in a.p series where a=14,d=(21-14)=7,l=84
let these no. are n
nth no. =a+(n-1)d=14+(n-1)*7=(7n+7)
7n+7=84,n=11.
answer C
Answer: C
Question: When 17 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: This means that 14 must be a multiple of k.
The factors of 14 are 1, 2, 7, and 14.
Out of these, k can be 7 and 14.
The answer is B.
Answer: B
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 123 hours, it must travel at a speed of:
Options:
A)234
B)377
C)720
D)378
E)268
Rationale: Speed and time are inversely proportional ⇒Speed ∝ 1Time (when distance is constant)
Here distance is constant and Speed and time are inversely proportionalSpeed ∝ 1Time⇒Speed1Speed2=Time2Time1⇒240Speed2=(123)5⇒240Speed2=(53)5⇒240Speed2=13⇒Speed2=240×3
=720 km/hr
Answer : D
Answer: D
Question: A computer factory produces 8400 computers per month at a constant rate, how many computers are built every 30 minutes assuming that there are 28 days in one month?
Options:
A)2.25.
B)3.125.
C)4.5.
D)5.225.
E)6.25.
Rationale: Number of hours in 28 days = 28*24
Number of 30 mins in 28 days = 28*24*2
Number of computers built every 30 mins = 8400/( 28*24*2) = 6.25
Answer E
Answer: E
Question: What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum ?
Options:
A)Rs. 112
B)Rs. 118.80
C)Rs. 120
D)Rs. 122
E)None
Rationale: Solution
Let the present worth be Rs. x. Then, S.I. = Rs. (132 - x).
∴ (x 5 x 2 /100)=132 - x =10x = 13200 - 100x= 110x = 13200 = x = 120.
Answer C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150
B)180
C)190
D)170
E)169
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: Option A
Answer: A
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 7.5), (8, 0), (0, -7.5), (-8, 0)?
Options:
A)56
B)88
C)112
D)116
E)120
Rationale: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 7.5+7.5= 15
Area= 1/2*16*15= 120
E is the answer
Answer: E
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is
Options:
A)289
B)231
C)200
D)288
E)111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
Answer: C
Answer: C
Question: The sum of 1 hours 45 minutes and 2 hours 55 minutes is approximately what percent of a day?
Options:
A)5%
B)10%
C)15%
D)20%
E)25%
Rationale: Since the question is asking for an approximate percentage
1:45+2:55 ~ 5 hours
% of day = 5*100/24 ~ 5*100/25= 20%
Answer is D.
Answer: D
Question: 15! is equal to which of the following?
Options:
A)1,307,674,368,000
B)1,307,674,368,242
C)1,307,674,368,356
D)1,307,674,368,825
E)1,307,674,368,624
Rationale: After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is A.
Answer: A
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.400 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)3999
B)7799
C)2500
D)5000
E)2912
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 400
B capital = 30000*1/6 = 5000.Answer: D
Answer: D
Question: Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
Options:
A)18
B)12
C)24
D)36
E)42
Rationale: let a=amount of 2% acid and b= amount of 12% acid.
Now, The equation translates to,
0.02a + .12b = .1(a+b)
but a+b= 60
therefore .02a + .12b = .1(60)
=> 2a + 12b = 600
but b=60-a
therefore
2a+ 12(60-a) = 600
=> 10a = 120
hence a = 12.
Answer : B
Answer: B
Question: Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 50 litres of tomato juice?
Options:
A)2.8 liters.
B)2.5 liters.
C)8.5 liters.
D)6.25 liters.
E)2.1 liters.
Rationale: Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
â‡’â‡’ 10%(50) = 80%(x)
â‡’â‡’ x = 6.25 liters.
Answer:D
Answer: D
Question: Out of 15 students in a class, 8 are wearing blue shirts, 4 are wearing green shirts, and 3 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
Options:
A)39/61
B)49/71
C)59/81
D)69/91
E)79/101
Rationale: Total possible ways to choose 4 students out of 15 = 15C4 = 1365
The number of ways to choose 4 students with no green shirts = 11C4 = 330
P(no green shirts) = 330/1365 = 22/91
P(at least 1 green shirt) = 1 - 22/91 = 69/91
The answer is D.
Answer: D
Question: A baseball team played 10 games and won 5. What is the ratio of the number of games played to the number of losses?
Options:
A)5:1
B)1:1
C)20:4
D)10:3
E)2:1
Rationale: The number of games played is 10. The number of games won is 5, so 10 - 5 = 5 = number of game losses.
Answer = !0:5 = 2:1
Answer is E
Answer: E
Question: A computer can perform z calculations in s seconds. How many minutes will it take the computer to perform k calculations?
Options:
A)ks/60z
B)ks/z
C)60ks/z
D)60z/ks
E)k/60zs
Rationale: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform z calculations in S seconds.
Let's TEST....
z = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
K = 80
So we're looking for an answer that = 2 when z = 2, S = 3 and K = 80
Answer A:KS/60z = (80)(3)/(60)(2) = 2 This IS a match
Answer B: KS/z = (80)(3)/2 = 120 This is NOT a match
Answer C: 60KS/z = 60(80)(3)/2 = 7200 This is NOT a match
Answer D: 60z/KS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: K/60zS = 80/(60)(2)(3) = a fraction. This is NOT a match
A
Answer: A
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 360 vote’s majority. What is the total number of votes polled?
Options:
A)750
B)700
C)900
D)850
E)None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 360 (40*9 = 360)
100% -----> 900 (100*9 = 900)
Answer: Option C
Answer: C
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 12 candidates. She plans to have one working interview with 3 of the 12 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
Options:
A)720
B)120
C)300
D)30
E)333
Rationale: 300.
Answer C
Answer: C