divelab/Sys2Bench huggingface dataset:
Question: Profits in the partnership of Bess, Bill and Bob are shared in the ratio 1 : 2 : 3. If Bill's share of the profits is $300, what is Bob's share?
Options:
A)$150
B)$900
C)$600
D)$450
E)None
Rationale: Ans is D
Given profit ratio, Bess : Bill : Bob = 1 : 2 : 3 To make Bill's portion $300, multiply by $150 => Bess : Bill : Bob = $150 : $300 : $450 => Bob's share = $450
Answer: B
Question: A, B and C enter into a partnership and theirs shares are in the ratio 1/2 : 1/3 : 1/4. After two months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B’s share?
Options:
A)Rs.129
B)Rs.144
C)Rs.156
D)Rs.168
E)Rs.178
Rationale: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
Therefore, B’s share = Rs. 378 * 8/21
= Rs.144.
ANSWER:B
Answer: B
Question: A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent
Options:
A)3488
B)7789
C)5400
D)2887
E)1881
Rationale: Explanation:
Interest for 1 year is the same whether it's simple interest or the compound interest.
Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225
if 100 is the principal interest =(1225/7350) * 100 = 50/3 %
When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100
Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %
Therefore amount after 2 years = 100 + 325/9 = 1225/9
If 1225/9 is the amount principal =100
if 7350 is the amount principal =(900/1225)*7350 =5400
So sum = 5400; Rate = 50/3 %
Answer: C) 5400
Answer: C
Question: Look at this series: 3, 1, (1/3), (1/9),... What number should come next?
Options:
A)1/27
B)1/18
C)1/61
D)2/27
E)None
Rationale: Explanation: This is a simple division series; each number is divisible by 3 of the previous number. In other terms to say, the number is divisible by 3 successively to get the next result.
9/3 = 3
3/3 = 1
1/3 = 1/3
(1/3)/3 = 1/9
(1/9)/3 = 1/27 and so on.
Answer: Option A
Answer: A
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?
Options:
A)10
B)36
C)38
D)40
E)42
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+2)(B+2) = m ----(2)
and
(L+6)(B+6) = m + 52 ---------> (L+6)(B+6) - 52 = m ------(3)
Equating (2) and (3)
(L+2)(B+2) = (L+6)(B+6) - 52
LB + 2L + 2B + 4 = LB + 6L + 6B + 36 -52
Simplify
4L + 4B = 20 ------> 2(L+B) = 10 (Check eq (1))
Answer is A
Answer: A
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 15th and the 20th terms?
Options:
A)324
B)335
C)346
D)357
E)379
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 15th term is 15 × 11 – 3 = 162
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 376
The correct answer is choice (E).
Answer: E
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are
Options:
A)12, 24, 30
B)12, 24, 38
C)12, 24, 362
D)12, 24, 36
E)12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12
\inline \fn_jvn \therefore The numbers are 12, 24, 36
Answer: D) 12, 24, 36
Answer: D
Question: How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
Options:
A)376
B)377
C)236
D)228
E)212
Rationale: The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
Answer: A
Answer: A
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
Options:
A)7/19
B)7/18
C)7/12
D)7/19
E)7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 7C2/`5C2 + 8C2/15C2
= 7/15
Answer: E
Answer: E
Question: 78, 64, 48, 30, 10, (...)
Options:
A)-12
B)-14
C)2
D)8
E)6
Rationale: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Answer: A
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 10 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
Options:
A)25
B)30
C)50
D)67
E)100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 10 oz can = 300 oz/10 oz = 30
Answer B, 30 cans
Answer: B
Question: The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is
Options:
A)15
B)n=25
C)35
D)30
E)none of these
Rationale: sum of 1st n natural no.s is n(n+1)/2,
sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,
The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))
=2(2n+1)/(3n(n+1))
now by hit and trial for the given options,if we put 25 then this will give 17/325
therefore the answer is 25
ANSWER:B
Answer: B
Question: An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
Options:
A)10
B)12
C)20
D)24
E)28
Rationale: First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with large notebooks.
The total number of different packages is 20.
The answer is C.
Answer: C
Question: How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Explanation:
We need so simple divide 42.5/0.85,
=(4250/85) = 50
Option C
Answer: C
Question: What is 120% of 13/24 of 360?
Options:
A)52
B)117
C)234
D)312
E)576
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 15 = 234
The answer is C.
Answer: C
Question: How many odd numbers between 10 and 1,000 are the squares of integers?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
14 numbers.
Answer: C.
Answer: C
Question: Two trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.
Options:
A)25 sec
B)23 sec
C)34 sec
D)22 sec
E)6 sec
Rationale: Explanation:
D = 150 m + 150 m = 300 m
RS = 95 + 85 = 180 * 5/18 = 50
T = 300 * 1/50 = 6 sec
Answer: Option E
Answer: E
Question: The duplicate ratio of 6:4 is?
Options:
A)1:2
B)9:4
C)1:8
D)1:18
E)1:13
Rationale: 36^2: 4^2 = 36:16=9:4
ANSWER:B
Answer: B
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
Options:
A)2877
B)5760
C)1797
D)1797
E)2972
Rationale: Explanation:
1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer:B
Answer: B
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 50 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
Options:
A)j/67
B)7j/500
C)140j
D)j/100+40
E)140j/100
Rationale: lets take j=1000, as decided by you..
now 50% increase makes it 1500..
this is the price for 100 jackets, so selling price for each jacket=1500/100=$15..
=j/67
so ans is correct as A..
Answer: A
Question: Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?
Options:
A)1/5
B)1/7
C)1/8
D)1/2
E)1/10
Rationale: Total cases are = 2^3=8
favoured cases =[TTH,THT,HTT,TTT]=4
Probability = 4/8=1/2
ANSWER D
Answer: D
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 14 kmph?
Options:
A)53.03
B)50.01
C)23.23
D)24.23
E)41.23
Rationale: distance covered in 1 min=(14*1000)/60=233.33m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=233.33/4.4=53.03
ANSWER:A
Answer: A
Question: Find number which is 70% less than 80.
Options:
A)18
B)22
C)24
D)26
E)98
Rationale: Explanation:
70% less is 30% of the given number
Therefore, 30% of 80 is 24.
ANSWER: C
Answer: C
Question: In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?
Options:
A)38
B)676
C)278
D)28
E)21
Rationale: Answer:B
Answer: B
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
Options:
A)3 (5/18)
B)3 (5/16)
C)3 (5/11)
D)3 (5/13)
E)3 (5/21)
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer:C
Answer: C
Question: The sum of money at compound interest amounts to thrice itself in 2 years. In how many years will it be 6 times itself?
Options:
A)8 years
B)9 years
C)2 years
D)6 years
E)4 years
Rationale: 100 ---- 300 --- 2
600 --- 2
----
4 years
Answer: E
Answer: E
Question: Three pounds of 05 grass seed contain 1 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide?
Options:
A)3
B)3.75
C)4.5
D)8.4
E)9
Rationale: 05 grass seed contains 5% herbicide and its amount is 3 pound
20 grass seed contains 20% herbicide and its amount is x
when these two types of grass seeds are mixed, their average becomes 15%
thus we have
3(1)+x(20)/(x+3) = 15
3+20x=15x +45
5x=42
or x=8.4
D
Answer: D
Question: One night 17 percent of the female officers on a police force were on duty. If 204 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)420
B)480
C)540
D)600
E)660
Rationale: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 102.
0.17x = 102
x = 600
The answer is D.
Answer: D
Question: The blood groups of 100 people is distributed as follows: 15 have type A blood, 20 have B blood type, 60 have O blood type and 5 have type AB blood. If a person from this group is selected at random, what is the probability that this person has AB blood type?
Options:
A)0.4
B)0.5
C)0.05
D)0.1
E)0.01
Rationale: Blood group -	frequency
A	- 15
B	- 20
O	- 60
AB	- 5
Let P(E) be the event of getting AB blood group
P(E) = Frequency for AB blood group / Total frequencies in the above table
= 5 / (5+60+20+15)
= 5 / 100
= 0.05
My answer is (C)
Answer: C
Question: A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get?
Options:
A)18 pounds
B)20 pounds
C)25 pounds
D)30 pounds
E)None of these
Rationale: Explanation:
Amount of rupees for exchange of 150 pounds = (150/100)*(7000/1) = Rs. 10,500
Out of these Rs.10,500, traveler spent Rs. 9060
Remaining balance in rupees = 10,500 – 9060 = Rs. 1440
Now these Rs. 1440 are exchanged back to pounds with the rate of 100 pounds for Rs. 7200
Amount in pounds = (1440 * 100) / 7200 = 20 pounds
ANSWER: B
Answer: B
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 80 times smaller, from source B alone?
Options:
A)6 hours and 40 minutes
B)15 minutes
C)12 minutes
D)10 minutes
E)5 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=80 times smaller or400/80=5 u
B will take 5/60 hrs or 5 minutes.
Ans E
Answer: E
Question: A is twice as good workman as B, and together they complete a work in 15 days. In how many days can the work be complete by B alone?
Options:
A)35 days
B)65 days
C)45 days
D)75 days
E)95 days
Rationale: C
45 days
Answer: C
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)8.8%
B)9%
C)9.2%
D)8.6%
E)8.4%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.12*15+0.08*35=4.6 kg, so the percentage is 4.6/50*100=9.2%.
Answer: C.
Answer: C
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)1/6
B)1/9
C)1/8
D)5/8
E)2/9
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E)=n(E)/n(S)
=4/36
=1/9
The answer should be B
Answer: B
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.70 per kg. What will be his gain percent?
Options:
A)8 1/7 %
B)2 1/3 %
C)11 2/3 %
D)8 1/8 %
E)8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.70
Gain % = 0.70/6 * 100 = 35/3
= 11 2/3 %
Answer:C
Answer: C
Question: There are 20 brown dogs, 10 white dogs, 15 black dogs.Totally how many dogs are there in all?
Options:
A)45
B)15
C)25
D)5
E)30
Rationale: 20+10+15=45. Answer is A
Answer: A
Question: The Guests at a football banquet consumed a total of 327 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
Options:
A)160
B)161
C)162
D)163
E)164
Rationale: To minimize one quantity maximize other.
163*2 (max possible amount of food a guest could consume) = 326 pounds, so there must be more than 163 guests, next integer is 164.
Answer: E.
Answer: E
Question: A goods train runs at the speed of 72 km/hr and crosses a 270 m long platform in 26 sec. What is the length of the goods train?
Options:
A)278
B)166
C)151
D)250
E)109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 270)/26 = 20
x = 250 m.
Answer:D
Answer: D
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options:
A)45
B)50
C)55
D)65
E)none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
∴ C’s rent = Rs. [175 * 9/35] = Rs. 45.
Answer A
Answer: A
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Options:
A)720 ways
B)735 ways
C)767 ways
D)723 ways
E)730 ways
Rationale: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer:A
Answer: A
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.13 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Options:
A)1276
B)1560
C)2832
D)1299
E)1236
Rationale: Explanation:
l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 13 = 1560
Answer: Option B
Answer: B
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Options:
A)450
B)470
C)560
D)700
E)510
Rationale: Let no. of non- officers be x
15 * 460 + x * 110 = (x + 15) 120
x = 510
E
Answer: E
Question: Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 60 m, then its area is??
Options:
A)2000 m^2
B)200 m^2
C)2520 m^2
D)2556 m^2
E)2534 m^2
Rationale: l -b = 10
2 (l+b)= 60 => l + b = 30
2 l = 40 => l = 20 so b = 10
area of the rectangle = l x b = 20 x 10 = 200 m^2
Answer : B
Answer: B
Question: The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 60. The bankerâ€™s discount is
Options:
A)Rs.960
B)Rs.840
C)Rs.1020
D)Rs.760
E)Rs.260
Rationale: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(60x100/10 x 3)
= Rs.200.
B.D
=Rs(200+ 60)
= Rs.260.
Answer E
Answer: E
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
Options:
A)124
B)129
C)132
D)142
E)144
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: C
Question: If a,b are positive integers and a/b=77.75 which of the following could be the value of b?
Options:
A)1. 25
B)2. 26
C)3. 27
D)4. 27
E)4. 32
Rationale: Given a/b = 77.75.
this is 77 and 3/4 = 311/4
Since a and b are integers we know that whatever is the value of b, it must be divisible by 4 completely(to make a an integer)
Ans:E
Answer: E
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
Options:
A)$5500
B)$11000
C)$22000
D)$2750
E)$44000
Rationale: Explanatory Answer
Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.
The extra interest earned on the compound interest bond = $ 55
The interest for the first year = $550/2 = $ 275
Therefore, the rate of interest = (55/275)*100 = 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest
If 20% of his investment in one of the bonds = $275, then his total investment in each of the bonds = (275/20)*100 = $ 1375
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = $ 2750.
correct choice is (D)
Answer: D
Question: How is 4% expressed as a decimal fraction?
Options:
A)0.4
B)0.04
C)0.004
D)0.0004
E)4
Rationale: 4/100= 0.04
ANSWER:B
Answer: B
Question: Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?
Options:
A)32
B)77
C)279
D)27
E)91
Rationale: Total five rounds were run. So in the final round 2 teams must have participated. In the penultimate round 4 teams, and 3rd round 8, 2nd round 16 and in the first round 32 teams must have participated as in each round half of the teams got eliminated.
Answer:A
Answer: A
Question: Two trains A and B are 175 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
Options:
A)10 s
B)6 s
C)4 s
D)8 s
E)13 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 175 + 150 = 325 m. Time taken =325/25 = 13 s.
CORRECT ANSWER E.
Answer: E
Question: In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 4 boys and 6 girls?
Options:
A)67
B)64
C)65
D)66
E)None of these
Rationale: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 64 ways in total.
B
Answer: B
Question: A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $204, what is the fewest number of $3 Frisbees that could have been sold?
Options:
A)24
B)12
C)8
D)52
E)2
Rationale: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 64
3x + 4y = 204
x = 64 - y
3(64-y) + 4y = 204
192 - 3y + 4y = 204
y = 12 x= 64-12= 52
D
Answer: D