divelab/Sys2Bench huggingface dataset:
Question: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
Options:
A)-4.5.
B)-2.
C)-1.7.
D)3.
E)2.5.
Rationale: Given : X+Y = 2X-2Z, --> eq 1
X-2Y = 4Z --> eq 2
X+Y+Z = 21 -->eq 3.
Now we are asked to find the value of Y/Z.
Now let choose some option randomly,
Take C , which is 3, I randomly chose this value as it is positive :)
Y/Z = 3 , this is the value we need to get.
Then Y = 3Z -- eq 4
Sub this in eq 1.
X + 3Z = 2X - 2Z
=> X = 5Z -->eq 5.
Sub X and Y value in eq 3.
5Z + 3Z + Z = 21
=> Z = 21/9. Now sub this value to get Y , we get Y = 21/3.
Then Y/Z = 21/3 / 21/9 = we get 3 again. So this option is correct.
Answer: option C is correct.
Answer: C
Question: A garrison of 150 men has provisions for 31 days. At the end of 16 days, a reinforcement arrives, and it is now found that the provisions will last only for 5 days more. What is the reinforcement?
Options:
A)150
B)450
C)400
D)600
E)300
Rationale: 150 ---- 31
150 ---- 15
x -----5
x*5 = 150*15
x = 450
150
-------
300
Answer: E
Answer: E
Question: The probability that a convenience store has no iced tea is 50%. If Karl is stopping by 2 convenience stores on his way to work, what is the probability thatat least oneof the stores will not have a can of iced tea?
Options:
A)1/8
B)1/4
C)1/2
D)3/4
E)7/8
Rationale: p=1-1/2^2(all stores have iced tea)=3/4
D
Answer: D
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)267 m
B)256 m
C)245 m
D)627 m
E)167 m
Rationale: Speed
= (45 * 5/18) m/sec = (25/2) m/sec. Time
= 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X)
= 750 ==> X
= 245 m.
Answer: C
Answer: C
Question: A searchlight on top of the watch-tower makes 3 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Rationale: 3 revolutions per minute = 1 revolution every 20 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 20 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 5 seconds) = 1 - P (man in dark for max of 5 seconds) = 1 - 5/20 = 1 - 1/4 = 3/4
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 20 seconds because that is the max. In this approach it would be 15/20 seconds = 3/4.
Answer: E
Question: A and B working saperately can do a piece of work in 12 and 18 hours respectively. If they work for 6 hour alternately with B beginning, in how many hours will the work be completed?
Options:
A)9 hours
B)15 hours
C)13 ½ hours
D)12 ½ hours
E)16 hours
Rationale: Explanation:
A and B 2 hours work = 1/12 + 1/18 = 5/36
work done by A and B during 6 pairs
i.e 12 hours = 6 * 5/36 = 5/6
Remaining work = 1 – 5/6 = 1/6
1/6 of work and this work done by B only = 18* 1/6 = 3 hours
Hence the total time take is 15 hours
Answer: Option B
Answer: B
Question: At the end of a business conference, ten people present shake hands with each other once. How many handshakes will be there all together?
Options:
A)20
B)45
C)55
D)90
E)None
Rationale: Explanation : . Total no. of handshakes = (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 45
Answer B
Answer: B
Question: What is the smallest of six consecutive odd integers whose average (arithmetic mean) is c + 2?
Options:
A)c - 5
B)c - 3
C)c- 1
D)c
E)c + 1
Rationale: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2
And 1st integer= 3rd integer- 4
let's say 3rd integer = n and 4th integer = n+2
2n+2/2= c+2
n= c+1
1st integer= c+1-4= c-3
B is the answer
Answer: B
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 1/9; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Options:
A)9/80
B)3/10
C)303/800
D)97/300
E)497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 1/30 = 29/30
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (29/30)(7/10) = 1 - 203/300 = 97/800
D
Answer: D
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)65 sec
B)89 sec
C)100 sec
D)150 sec
E)250 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec
ANSWER:B
Answer: B
Question: Which of the following does NOT have a divisor greater than 1 that is the square of an integer?
Options:
A)28
B)32
C)49
D)62
E)25
Rationale: Prime Factorization
28=2*2*7=2^2*7. Includes a perfect square of 4.
32=2*2*2*2*2=4^2*2. Includes the perfect square of 16.
49=7*7. Is a perfect square.
62=2*31. No perfect square here, so a possibility.
25= 5*5. Is a perfect square.
All but 62 have perfect squares as a factor so D is the correct answer.
28=2*2*7=2^2*7. Perfect square of 4.
32=2*2*2*2*2=4^2*2. Perfect square of 16.
49=7*7. Perfect square.
62=2*31. No perfect square.
25= 5*5. Perfect square.
Answer: D
Question: A 340-liter solution of Kola is made from 88% water, 5% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 10 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
Options:
A)6%.
B)7.5%.
C)9.2%.
D)10.5%.
E)11%.
Rationale: Denominator:
340+10+3.2+6.8=360
Numerator:
340(1-.88-.05)+3.2
340(0.07)+3.2
23.8+3.2
27
Ratio:
27/360=3/40
Answer: B
Answer: B
Question: 7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?
Options:
A)340
B)450
C)600
D)650
E)700
Rationale: Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.
∴ No. of books distributed in 1st day
= 7×5x+5×4x+8×2x=71x
No. of books distributed in 1Ind day
=7×5x+3×4x+5×2x=57x
And no. of books distributed in IIIrd day
=4×5x+5×4x+3×2x=46x
71x + 57x + 46x = 2000, x = 2000/174
57x=2000/174×57=650
D
Answer: D
Question: -24*29+1240=?
Options:
A)-544
B)584
C)544
D)345
E)None of these
Rationale: => -24*(30-1)+1240;
=> -(24*30)+24+1240;
=> -720+1264=544.
Correct Option: C
Answer: C
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)14
B)25
C)63
D)74
E)36
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
Ans: C
Answer: C
Question: What is the sum of the numbers between 1 and 12, inclusive?
Options:
A)99
B)65
C)79
D)78
E)80
Rationale: Sol. add the numbers between 1 and 12.
answer is D, 78.
Answer: D
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)8
B)9
C)5
D)3
E)2
Rationale: 2x * x = 128 => x
= 8
Answer:A
Answer: A
Question: If a(a + 2) = 99 and b(b + 2) = 99, where a ≠ b, then a + b =
Options:
A)-2
B)-5
C)-8
D)-10
E)-12
Rationale: i.e. if a = 9 then b = -11
or if a = -11then b = 9
But in each case a+b = -11+9 = -2
Answer: A
Answer: A
Question: A box contains 10 apples, 9 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: When you choose (and then eat) the first apple, the probability of that apple being red is 9/10. So if we do the activity 1 times, the probability of it being red is 9/10.
For 2 times, it is (9/10)*(8/9)
For 3 times, it is (9/10)*(8/9)*(7/8)
You can notice that the numerator of the first term cancels with the denominator of the second. So we can see that the probability becomes 0.5 when the last term is 5/6 & it becomes less than 0.5 when the last term is 4/5.
9 accounts for n=1, so 4 will account for n=6,
Answer.D
Answer: D
Question: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 1.50 + 1.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
Options:
A) $ 2.50
B) $ 3.00
C) $ 3.50
D) $ 6.00
E) $ 5.00
Rationale: Number of wheels in truck = 18
Number of wheels on its front axle =2
number of wheels remaining = 16
number of axles remaining axles = 16/4 = 4
Total number of axles = 5
T = 1.50 + 1.50( x − 2)
= 1.50 + 1.5*3
= 1.5 +4.5 = 6 $
Answer D
Answer: D
Question: If two of the four expressions x + y , x + 7y , x - y , and 7x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
Options:
A)1/3
B)1/8
C)1/2
D)1/6
E)1/5
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 7x and 7y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : D
Answer: D
Question: Triangle ATriangle B are similar triangles with areas 2268 units square and 2527 units square respectively. The ratio of there corresponding height would be
Options:
A)9:10
B)18:19
C)23:27
D)13:17
E)15:23
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=2268/2527
(x^2/y^2)=(18*18*7)/(19*19*7)
(x^2/y^2)=18^2/19^2
x/y=18/19
Ans=B
Answer: B
Question: Rajesh calculated his average over the last 24 tests and found it to be 76. He finds out that the marks for three tests have been inverted by mistake. The correct marks for these tests are 87, 79 and 98. What is the approximate percentage difference between his actual average and his incorrect average?
Options:
A)0
B)9
C)8
D)7
E)5
Rationale: No Change
Incorrect value is: 78, 97, 89
correct values are: 87, 79, 98
difference between correct and incorrect value is= 9 + 9 -18=0
Answer:A
Answer: A
Question: Given that -1 ≤ v ≤1, -2 ≤ u ≤ -0.5 and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true ?
Options:
A)-0.5 ≤ w ≤ 2
B)-4 ≤ w ≤ 4
C)-4 ≤ w ≤ 2
D)-2 ≤ w ≤ 0.5
E)None of these
Rationale: Explanation :
We try to get an upper bound on the value of w.
After taking a look at the options we figure it out that if we take v=-1,z=-2 and u=-0.5.
we get the lower bound as -4.
If we take v=1, z=-2 and u=-0.5 we have the upper bound as 4.
Hence, the right option is 2.ie -4 ≤ w ≤ 4
Answer : B
Answer: B
Question: A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
Options:
A)8
B)12
C)15
D)21
E)27
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15
B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12
A+B=15+12=27
Answer: E.
Answer: E
Question: Mars travels around the sun at a speed of approximately 15 miles per second. The approximate speed is how many miles per hour?
Options:
A)48,000
B)51,000
C)54,000
D)57,000
E)60,000
Rationale: 15 * 3600 = 54,000
The answer is C.
Answer: C
Question: Find a a prime number from below options?
Options:
A)84
B)97
C)98
D)100
E)102
Rationale: Clearly, 97 is a prime number.
B
Answer: B
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 160 kilometers?
Options:
A)4
B)5.5
C)6.5
D)7.5
E)8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 160 kilometers?
160 ÷ 40 = 4 × 1 gallon = 4 gallons
correct answer A
Answer: A
Question: On a summer camp, 25% of the campers paid $120 each, 30% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
Options:
A)18%
B)21%
C)35%
D)33.3%
E)37.5%
Rationale: let the total no of campers be 100
total amount = (25*120)+(30*80)+(40*65) = 3000+2400+2600= $8000
required percentage = (28/80)*100 =35%
C
Answer: C
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
Options:
A)3:8
B)3:9
C)3:4
D)3:12
E)4:12
Rationale: Water:soap = 3:4
Soap:Salt=12:16
=> For 12 soap, salt = 16
=> For 4 Soap, salt = (16/12)*4 = 16/12=64/12=18/3=6/1
So, water:soap:salt = 3:4:6 = 3:4:6
After open container, water:soap:salt = 1.5:4:6
So, water:salt = 1.5:6 = 3:12
ANSWER:D
Answer: D
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 07:00 and starts climbing at a constant pace. Ken starts climbing only at 09:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
Options:
A)13:00
B)13:30
C)14:00
D)15:00
E)15:30
Rationale: Both Sari and Ken climb in the same direction.
Speed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs
Starting from 9:00, in 5 hrs, the time will be 14:00
Answer (C)
Answer: C
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.51200?
Options:
A)81000
B)81028
C)27772
D)29889
E)64800
Rationale: 51200* 9/8 * 9/8 = 64800.Answer:E
Answer: E
Question: Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
Options:
A)(1/3)
B)(1/8)
C)(2/8)
D)(1/16)
E)(1/32)
Rationale: Answer: Option B
This is a simple division series; each number is one-half of the previous number.
In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8
Answer: B
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 12 km per hour and the level part at the rate of 18 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 18 km per hour for the entire route?
Options:
A)24
B)30
C)36
D)42
E)48
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 18 km/hour
3D / (D/12 + D/18 + D/V) = 18
1/6 = 1/12 + 1/18 + 1/V
1/V = 1/36 and so V = 36 km/h
The answer is C.
Answer: C
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 67.5% percent carbonated water, what percent of the volume of the mixture is P?
Options:
A)25%
B)40%
C)50%
D)60%
E)75%
Rationale: 67.5% is 12.5%-points below 80% and 12.5%-points above 55%.
So the ratio of solution P to solution Q is 1:1.
Mixture P is 1/2 = 50% of the volume of mixture PQ.
The answer is C.
Answer: C
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)72%
B)82%
C)12%
D)22%
E)42%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: C
Question: The ratio between the present ages of P and Q is 6:7.If Q is 4 years old than P,what will be the ratio of the ages of P and Q after 4 years ?
Options:
A)3:4
B)3:5
C)4:3
D)None of these
E)Cannot be determined
Rationale: Solution
Let P's age and Q's age be 6x years and 7x years respectively.
Then,7x-6x = 4 ⇔ x = 4.
∴ Required ratio = (6x + 4) : (7x + 4)=28 : 32 =7: 8. Answer D
Answer: D
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Options:
A)1008
B)1015
C)1022
D)1032
E)1048
Rationale: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Answer: Option B
Answer: B
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
Options:
A)7½ sec
B)10 sec
C)12 ½ sec
D)15 sec
E)18 sec
Rationale: Speed of train = 132 *(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (110 + 165) m = 275 m.
Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec
Answer : A.
Answer: A
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 1/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
Options:
A)1/20
B)3/40
C)13/40
D)7/20
E)13/22
Rationale: P(1 and not 2)=1/8*(1-3/5)=1/20.
Answer: A.
Answer: A
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 70
II. 50
III. 92
Options:
A)I only
B)III only
C)I and II
D)I only III
E)II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 70--> Not possible
II. 50 --> 12 + 38-->Possible
III. 92 --> 30 + 622 --> Possible
Answer: E
Answer: E
Question: When n is divided by 5 the remainder is 3. What is the remainder when (n + 2)^2 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: n = 5x+3, for some integer x
(n+2)^2=(5x+5)^2=5y, for some integer y
When we divide this by 5, the remainder is 0.
The answer is A.
Answer: A
Question: A man sells a horse for Rs.800 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)287
B)279
C)267
D)860
E)298
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x
= 60
CP = 800 + 60
= 860
Answer:D
Answer: D
Question: The ratio between the speeds of two Bullet trains is 7:6. If the second Bullet train runs 440 kms in 4 hours, then the speed of the first train is:
Options:
A)89.25 km/hr.
B)37.25 km/hr.
C)128.3 km/hr.
D)94.25 km/hr.
E)96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 6x km/hr.
Then, 6x = (440/4) = 110
x = (110/6) = 18.33
Hence, speed of first bullet train = (7 x 18.33) km/hr = 128.3 km/hr.
C
Answer: C
Question: In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
Options:
A)1000
B)3000
C)3500
D)2500
E)2250
Rationale: For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is 1000
Answer: A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
Options:
A)Rs.4082.87
B)Rs.4082.42
C)Rs.4082.97
D)Rs.4082.40
E)Rs.4082.19
Rationale: Length of the first carpet
= (1.44)(6) = 8.64 cm
Area of the second carpet
= 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m
= (12.96)(7) sq m
Cost of the second carpet
= (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6
= Rs.4082.40
Answer:D
Answer: D
Question: A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
Options:
A)20
B)25
C)30
D)35
E)40
Rationale: Let x be the number of additional games the gambler needs to play.
0.4(30) + 0.8x = 0.6(x+30)
0.2x = 6
x = 30
The answer is C.
Answer: C
Question: Find the no.of ways of arranging the 10 boys around a round tabele?
Options:
A)9!
B)10!
C)8!
D)7!
E)6!
Rationale: Ans.(9!)
Sol. Total number of persons = (10-1)! =9!
Answer: A
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $560 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A)23,500
B)24,000
C)25,500
D)26,500
E)27,500
Rationale: Let the weekly sales of both = x
560+(x−1000)8/100=10/100x
x = 24000
ANSWER:B
Answer: B
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 5 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Options:
A)187 km
B)480 km
C)278 km
D)297 km
E)600 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 5
2x/15 - x/8 = 5 => x = 600 km.
Answer:E
Answer: E
Question: Shan starts from Barabanki to Fatehpur, 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shan is at least 20km/hour fasterthan the speed of Kajol. What is the min speed of Shan to overtake Ajay, before he meets Kajol?
Options:
A)40.5 km/h
B)45.67 km/h
C)50.7 km/h
D)68.5 km/h
E)67.5 km/h
Rationale: Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
E)
Answer: E
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 300 men leave the temple, how long will the food last now?
Options:
A)25 1/2 days
B)29 1/2 days
C)28 1/2 days
D)27 1/2 days
E)26 1/2 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1300*x
x =29 1/2 days
ANSWER:B
Answer: B
Question: There is a 10% chance that Tigers will not win at all during the whole season. There is a 5% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?
Options:
A)A)55%
B)B)60%
C)C)70%
D)D)72%
E)E)95%
Rationale: There is a 10% chance that Tigers will not win at all during the whole season
We can infer that there is 90% chance Tigers will win .
Similarly There is a 5% chance that Federer will not play at all in the whole season
We can also infer that there is 95% chance that Federer will play.
Answer E
Answer: E