divelab/Sys2Bench huggingface dataset:
Question: When x is divided by y, the quotient is z with remainder r. Which of the following is equal to r?
Options:
A)yz – x
B)y/x−z
C)x – y – z
D)x – yz
E)zx – y
Rationale: (x/y)=z(+r)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: D
Question: A miniature gumball machine contains 4 blue, 3 green, and 2 red gumballs, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
Options:
A)2/7
B)3/7
C)3/14
D)5/24
E)7/24
Rationale: The total number of ways to dispense 3 gumballs is 9C3=84.
The number of ways to choose one of each color is 4*3*2=24.
P(dispensing one of each color)=24/84=2/7.
The answer is A.
Answer: A
Question: In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ?
Options:
A)22
B)27
C)75
D)29
E)271
Rationale: Explanation:
Let the number of students in the class be 100 and let this required average be x.
Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80)
=> 70x = 8000 - (950 + 1800) = 5250
=> x = 75.
Answer: C) 75
Answer: C
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many
men will be catered to with the remaining meal ?
Options:
A)38 men
B)32 men
C)34 men
D)30 men
E)None of these
Rationale: Explanation:
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 120 men
So, 50 Children = 120/200 * 50 = 30 men
Answer: D
Answer: D
Question: A car is purchased on hire-purchase. The cash price is $25 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
Options:
A)$500
B)$504
C)$505
D)$560
E)$600
Rationale: Explanation:
Cash price = $25 000
Deposit = 10% Ã— $25 000 = $2500
Loan amount = $25000 âˆ’ $2500
Number of payments = 60
= $22500
I=p*r*t/100
I=13500
Total amount = 22500 + 13500 = $36000
Regular payment = total amount /number of payments =600
Answer: E
Answer: E
Question: The ratio between the presents of the A and B is 6:7. If B is 4 years older than A, what will be the ratio of the ages of A and B after 4 years?
Options:
A)1:2
B)9:11
C)7:8
D)6:7
E)3:4
Rationale: Let A and B ages will be 6x and 7x
7x - 6x = 4
x = 4
Required ratio = 6x+4 : 7x+4 = 28:32 = 7:8
Answer is C
Answer: C
Question: The salary of A, B, C, D, E is Rs. 10000, Rs. 5000, Rs. 11000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
Options:
A)Rs. 7000
B)Rs. 8400
C)Rs. 8500
D)Rs. 9000
E)None
Rationale: Answer
Average salary
= 10000 + 5000 + 11000 + 7000 + 9000 / 5
= Rs. 8400
Correct Option: B
Answer: B
Question: The triplicate ratio of 1:8 is?
Options:
A)1:0
B)1:8
C)1:7
D)1:512
E)1:1
Rationale: 13: 83 = 1:512
Answer: D
Answer: D
Question: The length of the bridge, which a train 110 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)328
B)279
C)265
D)288
E)211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (110 + X)/30 = 25/2 ==> 2(110 + X) = 750 ==> X = 265 m.Answer: C
Answer: C
Question: A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?
Options:
A)days
B)days
C)days
D)days
E)days
Rationale: Explanation:
(man + boy)’s 1 day’s work = 1/24
Their 20 day’s work = 1/24 × 20 = 5/6
The remaining 1/6 work is done by the man in 6days
Therefore, the man alone will finish the work in 6 × 6 days = 36 days
Man’s 1 day’s work = 1/36
Therefore, boy’s 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72
Therefore, the Boy alone will finish the work in 72 days.
Answer: Option A
Answer: A
Question: Pinky bought six Chocolate at an average price (arithmetic mean) of 5¢. If Pinky returned four chocolate to the retailer, and the average price of the remaining chocolate was 2¢, then what is the average price, in cents, of the four returned chocolates?
Options:
A)6.5
B)5.5
C)4.5
D)5
E)6.4
Rationale: Total price of 6 chocolates=6*5=30
Total price of 2 chocolates=2*2=4
Total price of 4 returned chocolates=30-4=26
Average price of 4 returned chocolate=26/4=6.5
Correct option Answer:A
Answer: A
Question: John makes $30 a week from his job. He earns a raise andnow makes $40 a week. What is the % increase?
Options:
A)16%
B)33.33%
C)33.69%
D)33.98%
E)37%
Rationale: Increase = (10/30)*100 = (1/3)*100 = 33.33%.
B
Answer: B
Question: The avearage age of boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is
Options:
A)15 years
B)15.5 years
C)16 years
D)Cannot be computed
E)None of these
Rationale: Solution
Clearly, to find the average,we ought to know the numbers of boys , girls or students in the class, neither of which has been given.
so the data provided is inadequate.
Answer D
Answer: D
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 5 ------------------------------------------ 5,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 8 ------------------------------------------ 17,000
S4 ---------------------- 7 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?
Options:
A)14
B)20
C)22
D)30
E)25
Rationale: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 25/50000 or 1 every 2000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/2000) * 60000 = 30
D
Answer: D
Question: A classroom has equal number of boys and girls. NINE girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
Options:
A)36
B)24
C)32
D)48
E)54
Rationale: after 9 girls left remaining 9 girls
now boys 18 are twice as many as remaining girls.
initially boys=18 and girls=18.
ANSWER:A
Answer: A
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
Options:
A)31.11 km/hr
B)35.55 km/hr
C)71.11 km/hr
D)36 km/hr
E)71 km/hr
Rationale: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 320 x 2/9 = 71.11 km/hr.
Answer : C.
Answer: C
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 95 students?
Options:
A)14 years
B)1.7 years
C)1.9 years
D)2.8 years
E)None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 95
= 2.8years.
Answer D
Answer: D
Question: What decimal fraction is 40 ml of a litre ?
Options:
A).4
B).04
C).05
D)0.04
E)None of these
Rationale: Answer
Required fraction = 40/1000
= 4/100
= .04
Correct Option: B
Answer: B
Question: A certain manufacturer sells its products	to stores in 113 different	regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an	average of 51,750 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product	sold	worldwide last	year?
Options:
A)10^5
B)10^6
C)10^7
D)10^8
E)10^9
Rationale: 51750*181*113 or
51000*180*113 or
50000*200*100
=10^9
E
Answer: E
Question: Rajani, Roja and Ramani share a sum of money in the ratio 7 : 8 : 16. If Ramani receives Rs. 27 more than Rajani, then the total money shared was:
Options:
A)Rs 33
B)Rs 49
C)Rs 93
D)Rs 69
E)Rs 77
Rationale: Explanation :
Let Rajani = 7x, Roja = 8x & Ramani = 16x. Then, total money = 31x.
Now, Ramani - Rajani = 27 so 16x7x = 27 that is why x = 3.
Total money 31*x = Rs.93.
Answer : C
Answer: C
Question: The positive numbers w, x, y, and z are such that x is 35 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?
Options:
A)15.2%
B)16.0%
C)20.0%
D)23.2%
E)24.8%
Rationale: My strategy is same as theDobermanbut instead take z=100, which makes life a bit easy. As:
z=100
y=120 (20% greater than z)
z=144(20% greater than y)
Now calculate w 20% less than z = 144*80/100= 115.2
Now by just looking, relation between w and z:
w-z/z*100 = 20 - Answer C
Answer: C
Question: What is the average (arithmetic mean) of the numbers 21, 22, 23, 23, 24, and 25?
Options:
A) 23.0
B) 22.5
C) 21
D) 24
E) 23
Rationale: {21, 22, 23, 23, 24, 25}={23-2,23-1, 23, 23,23+1,23+2} --> the average = 23.
Answer: E.
Answer: E
Question: A train covers a distance of 12 km in 10 min. If it takes 2 sec to pass a telegraph post, then the length of the train is?
Options:
A)40
B)80
C)120
D)60
E)20
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 2 = 40 m.
Answer: Option A
Answer: A
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
Options:
A)21/46
B)25/117
C)1/50
D)3/25
E)None of these
Rationale: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=	(25 x 24 x 23)/(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
=	[10 x	((15 x 14)/(2 x 1))]
= 1050.
P(E) =n(E)/n(S)=1050/2300=21/46	.
Answer :A
Answer: A
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
Options:
A)1/3
B)1/5
C)1/7
D)1/9
E)2/3
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A
Answer: A
Question: Three friends (Sarah, Jane and Gina) are employees of a company. Their respective salaries are in the ratio of 1 : 3 : 7. Jane and Gina's salaries together is Rs. 7000. By what percent is Gina's salary than that of Sarah?
Options:
A)200%
B)600%
C)100%
D)300%
E)400%
Rationale: Explanation:
Let the salaries be x, 3x and 7x respectively.
Then,3x + 7x = 7000 => x = 700.
Sarah's salary = Rs. 700, Jane's salary = Rs. 2100, and Gina's salary Rs. 4900.
Excess of Gina's salary over Sarah's=[ (4200 /700) x 100] = 600%.
Answer: B
Answer: B
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)42 sec
C)45 sec
D)48 sec
E)49 sec
Rationale: total length= 360+140=500
speed=45km/h=(45*5)/18= 25/2m/s
time=(500*2)/25=40 sec.
ANSWER:A
Answer: A
Question: A cyclist covers a distance of 750m in 2 min 30sec. What is the speed in km/hr of the cyclist?
Options:
A)18
B)15
C)9
D)5
E)10
Rationale: distance = 750 m
time = 2min 30 sec = 150 sec
speed = (750/150) m/s = 5m/s
speed in km/hr = 5*18/5 = 18 km/hr
correct option is A
Answer: A
Question: Naresh’s monthly income is 30% more than that of Raghu. Raghu’s monthly income is 20% less than that of Vishal. If the difference between the monthly incomes of Naresh and Vishal is 800, what is the monthly income of Raghu?
Options:
A)16,000
B)20,000
C)12,000
D)Data inadequate
E)None of these
Rationale: N = R + 30% of R = 1.3 RR
= V – 20% of V = 80% of V = 0.8 V
∴ N = 1.3 × 0.8V = 1.04 V
Now, N – V = 1.04 V – V = 0.04 V = 800(given)
∴ V = 20000
∴ R = 0.8 × 20000 = 16000
Answer A
Answer: A
Question: A car moves at 45 km/hr. What is the speed of the car in meters per second ?
Options:
A)12 1/2 m sec
B)12 2/9m sec
C)14 1/9m sec
D)16 1/2m sec
E)18 2/9m sec
Rationale: Explanation:
Speed=(45∗5/18)m/sec
=25/2 m/sec
=12 1/2 msec
Option A
Answer: A
Question: 1, 9, 17, 33, 49, 73, ?
Options:
A)81
B)83
C)85
D)97
E)91
Rationale: The pattern is + 8, + 8, + 16, + 24,...
Answer : D.
Answer: D
Question: Robert ate 7 chocolates, Nickel ate 3 chocolates. How many more chocolates did Robert ate than nickel?
Options:
A)4
B)7
C)9
D)5
E)2
Rationale: 7-3=4. Answer is A
Answer: A
Question: The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $21. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
Options:
A)347.8
B)987.8
C)877.8
D)898.8
E)667.4
Rationale: Let the costs of each kg of mangos and each kg of rice be $a and $r respectively.
10a = 24r and 6 * 21 = 2r
a = 12/5 r and r = 63
a = 151.2
Required total cost = 4 * 151.2 + 3 * 63 + 5 * 21
= 604.8 + 189 + 105 = $898.80
D
Answer: D
Question: Which of the following must be true?
1) Every prime number greater than 5 can be written as either as 8n+1 or 8n-1
2) Every prime number greater than 5 can be written as 4n+1 or 4n-1
3) Every number greater than 5 of the form 8n+1 or 8n-1 is a prime number.
Options:
A)1,2,3
B)2,3
C)1,2
D)only 1
E)only 2
Rationale: Every prime number greater than 3 can be written in the form of 8n+1 or 8n-1 where n is an integer. So 1 can be possible.
3. This is not possible as 2 and 3 are being prime , we can't write then in the form of 8n+1 or 8n-1.
C
Answer: C
Question: The organizers of a week-long fair have hired exactly seven security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 guards will be available to patrol the fairgrounds on the following Saturday night?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 4 guards.
To choose 3 out of 4, we will have 4C3 = 4 different groups.
The answer is B.
Answer: B
Question: If a certain sample of data has a mean of 23.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)17.0
D)15.5
E)26.5
Rationale: The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is D.
Answer: D
Question: 5+5 = 10
38+20 = 1858
5+3 = 28
9+1 = 810
8+6 = 214
5+4 = 19
7+3 = ?
Options:
A)400
B)410
C)420
D)430
E)440
Rationale: equence is like that first the sum of digits is written then subtraction of digits is written....ex 5+5=10 solution:5-5=0,5+5=10...same way 7+3=10and 7-3=4
so 7+3=410..
ANSWER:B
Answer: B
Question: city A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)57
B)57.5
C)56
D)59
E)60
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: B
Question: Calculate the different number of ways 5 boys and 2 girls can sit on a bench?
Options:
A)6040
B)5030
C)5140
D)5010
E)5040
Rationale: npn = n!
7p7 = 7 × 6 × 5 × 4 × 3 × 2 × 1= 5040
E
Answer: E
Question: add 15% of 25 and 12% of 45.
Options:
A)9.2
B)10.5
C)11.5
D)12.3
E)15
Rationale: 15% of 25 + 12% of 45
25*15/100+45*12/100
3.8+5.4=9.2
answer A
Answer: A
Question: A and B complete a work in 8 days. A alone can do it in 12 days. If both together can do the work in how many days?
Options:
A)3.75 days
B)3.99 days
C)2.99 days
D)4.8 days
E)2.44 days
Rationale: 1/8 + 1/12 = 5/24
24/5 = 4.8 days
Answer: D
Answer: D
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 30 square meters. What is the area that is covered with three layers of wallpaper?
Options:
A)5 Square Meters
B)36 Square Meters
C)42 Square Meters
D)45 Square Meters
E)120 Square Meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 30= 90 sq m of the wallpaper overlaps in three layers. 90 sq m makes two extra layers hence the area over which it makes two extra layers is 45 sq m.
Answer (D).
Answer: D
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20
B)77
C)66
D)55
E)31
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: A
Question: (X% of Y) +(Y% of X) is equal to:
Options:
A)X% of Y
B)20% of XY
C)2% of XY
D)2% of 100 XY
E)None
Rationale: Solution: According to question,
(XY /100) + (YX /100)
= 2XY /100
= 2% of XY.
Answer: Option C
Answer: C
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percent?
Options:
A)8 1/8 %
B)8 3/3 %
C)8 1/3 %
D)2 1/3 %
E)8 6/3 %
Rationale: Explanation:
C.P. of 1 kg = 420/7 = Rs. 6
S.P. of 1 kg = Rs. 6.50
Gain % = 0.50/6 * 100 = 25/3 = 8 1/3 %
Answer: C
Answer: C
Question: What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?
Options:
A)34
B)42
C)47
D)58
E)79
Rationale: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).
In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.
i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0
or −27+36+21+12=k−27+36+21+12=k
or k=k= 42
B
Answer: B
Question: If cost of 15 eggs be 70 rupees, then find out the cost of 5 dozen eggs.
Options:
A)276
B)400
C)500
D)600
E)700
Rationale: Cost of 15 eggs = 70 rupees
Cost of 1 egg = 70/15 = 4.6 rupees,
Cost of 5 dozens, i.e. 4.6 x 12 = 55.2 x 5 = 276
Answer : A
Answer: A
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)88
B)99
C)62
D)27
E)12
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88
Answer:A
Answer: A
Question: 4 + 4 + 4 + 2 × 4^2 + 2 × 4^3 + 2 × 4^4 + 2 × 4^5 + 2 × 4^6 + 2 × 4^7 =
Options:
A)4^12
B)4^16
C)4^7
D)4^13
E)4^10
Rationale: We have the sum of 9 terms. Now, if all terms were equal to the largest term 2*4^7 we would have: sum=9*(2*4^7)=18*4^9=~4^11, so the actual sum is less than 4^11 and more than 4^7 (option C) as the last term is already more than that. So the answer is clearly E.
Answer: E
Answer: E
Question: Jason flips a coin three times. What is the probability B that the coin will land on the same side in all three tosses?
Options:
A)1/16
B)1/8
C)1/4
D)1/3
E)1/2
Rationale: Total outcome is 2^3=8
Favorable cases HHH or TTT
Therefore, probability B is 2/8 or 1/4.C
Answer: C
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 1 out of 5 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
Options:
A)2/25
B)4/75
C)2/75
D)3/5
E)4/5
Rationale: Probability of sand dune blown out = 2/3
Probability that it has treasure = 1/5
Probability that it has lucky coupon = 1/5
total probability = 2/3 * 1/5 * 1/5 = 2/75
ANSWER:C
Answer: C
Question: A girl purchased “m” number of pens of type “A” at the unit price of “Rs. x” each, “n” number of pens of type “B” at the unit price of “Rs. y” each and “p” number of pens of type “C” at the unit price of “Rs. z” each. Which of the following represents the average price of all the pens taken together?
Options:
A)(mx + ny + pz) / (m + n + a)
B)(mx + ny + pz) / (m + n + G)
C)(mx + ny + pz) / (m + n + p)
D)(mx + ny + pz) / (m + n + b)
E)(mx + ny + pz) / (m + n + t)
Rationale: Explanation:
(mx + ny + pz) / (m + n + p)
Required Average = Total Price / Total number = (mx + ny + pz) / (m + n + p)
ANSWER: C
Answer: C
Question: Two hundred multiples of seven are chosen at random, and 300 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
Options:
A)20%
B)25%
C)40%
D)50%
E)80%
Rationale: Two hundred multiples of seven will have 100 even and 100 odd numbers
300 multiples of eight will have ALL even (being multiple of 8)
Probability of number selected being odd = Total Odd Numbers / Total available numbers
Probability = 100/500 = 0.2 = 20%
Answer: Option A
Answer: A
Question: A man walked a certain distance south and then the same distance plus 7km due west.He is now 13km from his starting point.What are the distances south and west that he walked?
Options:
A)5,12
B)6,12
C)7,12
D)5,13
E)6,13
Rationale: If a man walked distance(in km) 'x' towards south & then 'x+7'towards west.
Distance from starting point=Hypotenuse of a right triangle with sides x & (x+7)
So 13^2=x^2+(x+7)^2
x^2+7x-60=0 or (x+12)(x-5)=0, so x=5
Distance towards west=x+7=5+7=12 km.
ANSWER:A
Answer: A
Question: Molly can do a task in 20 days while Sandy can do the task in 30 days. How many days will it take to complete the task if both work together?
Options:
A)8
B)9
C)10
D)12
E)15
Rationale: Each day, Molly can do 1/20 of the task.
Each day, Sandy can do 1/30 of the task.
Each day, they can do 1/20 + 1/30 = 1/12 of the task.
The task will be completed in 12 days.
The answer is D.
Answer: D
Question: By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
Options:
A)7
B)7.5
C)8
D)9
E)10
Rationale: Explanation:
Marked price = Rs. 300
C.P. = 100/120 * 300 = Rs. 250
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 20/250 * 100 = 8%.
ANSWER IS C
Answer: C
Question: The maitre 'd at an expensive Manhattan restaurant has noticed that 60% of the couples order dessert and coffee. However, 20% of the couples who order dessert don't order coffee. What is the probability W that the next couple the maitre 'd seats will not order dessert?
Options:
A) 20%
B) 25%
C) 40%
D) 60%
E) 75%
Rationale: could you use a venn diagram and just go with the number 100.
60 people order dessert and coffee... which is the union of D and C.
W=2/10 of D aren't in D U C = so 8/10 of D are in DUC which means =60 =8/10D. So D in total=75, and 15 D's aren't in D union C. which means 25 people are in C only + Neither.
B 25%
Answer: B
Question: The time on a clock is 20 minutes past 3. What is the angle between the hands of the clock?
Options:
A)60 degrees
B)20 degrees
C)45 degrees
D)50 degrees
E)30 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 100 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 120 - 100 = 20 degrees.
The answer is B.
Answer: B
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 16 km in stationary water
Options:
A)40 min
B)1hr
C)1hr 15 min
D)1hr 30 min
E)4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(16/4)= 4hr
Answer(E)
Answer: E