divelab/Sys2Bench huggingface dataset:
Question: A box contains 90 nuts each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg., then the weight of the empty box is
Options:
A)8
B)9.5
C)10
D)11.5
E)12
Rationale: Let w(e) be weight of empty box.
Total weight = 35.5 Kg
Weight of nuts, w(n) = 90 * 100 = 9000gms = 9 kg
Weight of bolts, w(b) = 100 * 150 = 15000gms = 15 kg
Total weight = w(n)+w(b)+w(e)
w(e) = Total weight-w(n)-w(b)
=> w(e) = 35.5-15-9=11.5 Answer : D
Answer: D
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008 ?
Options:
A)Monday
B)Tuesday
C)wednesday
D)Sunday
E)None of these
Rationale: Solution
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday. Answer B
Answer: B
Question: a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 4a = 2b = c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
Options:
A)124
B)297
C)394
D)421
E)842
Rationale: Ratio of a:b:c= 1:2:4
Two possible greatest single digit values for c are 8 and 4
if c is 8, then x= 248
if c is 4, then x= 124
difference= 248-124= 124
A is the answer
Answer: A
Question: If (c - a)/(c - b) = 1, then (5b - 2a)/(c - a) =
Options:
A)0.5
B)1
C)1.5
D)2
E)6
Rationale: Let's say c=3, b=2, a=2 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 6
Answer E (hopefully )))
Answer: E
Question: Michael cashed a check for $1,300 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
Options:
A) $830
B) $800
C) $770
D) $730
E) $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1300 - 470 = 830.
Answer A
Answer: A
Question: A baseball team won 55 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
Options:
A)36
B)45
C)50
D)55
E)37
Rationale: Games won out of first 80 questions = (55/100)*80 = 44
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-44 = 37
Answer: Option E
Answer: E
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
Options:
A)1452
B)1243
C)1564
D)1296
E)1234
Rationale: Number of rectangles that can be formed by using m horizontal lines and n vertical lines
= mC2 × nC2
Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)2
=(9×82×1)2=362=1296=(9×82×1)2=362=1296
Ans: D
Answer: D
Question: In the coordinate plane, Line A has a slope of -2 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The equation of Line A is y = -2x + 4
The equation of Line B is y = 5x - 10
5x - 10 = -2x + 4
x = 2
y = 0
The point of intersection is (2,0) and then a+b = 2.
The answer is C.
Answer: C
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
Options:
A)29
B)28
C)54
D)27
E)21
Rationale: D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph.Answer: C
Answer: C
Question: How many numbers between 190 and 580 are divisible by 4,5 and 6?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Every such number must be divisible by L.C.M of 4,5,6 i.e, 60.
Such numbers are 240,300,360,420,480,540.
Clearly, there are 6 such numbers
ANSWER:A
Answer: A
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)3 : 5 : 2
B)3 : 5 : 5
C)6 : 10 : 5
D)Data inadequate
E)None
Rationale: EXPLANATION
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer C
Answer: C
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 20 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)x/12%
D)300/x%
E)500/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 20 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 3 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 3 miles at 60 miles per hour (5 minutes).
Now, plug x = 3 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: D.
Answer: D
Question: The equation x = 2y^2 + 5y - 16, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
Options:
A)3x + y + 15 = 0
B)y + 3x - 1 = 0
C)-3x + y - 16.5 = 0
D)-2x - y - 7 = 0
E)-3x + y + 13.5 = 0
Rationale: The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B , if you put x = -5, you get -ve value for y co-ordinate.
Answer must be (B)
Answer: B
Question: If four coins are tossed, the probability of getting heads only?
Options:
A)4/16
B)2
C)1/16
D)2/16
E)3/16
Rationale: Since four coins are tossed, sample space = 16
Getting heads=1
p(E) = 1/16
ANSWER:C
Answer: C
Question: Rs.1040 is divided amongst A, B, C so that 2 times A's share, 3 times B's share and 4 times C's share are all equal. Find A's share?
Options:
A)177
B)150
C)817
D)480
E)616
Rationale: A+B+C = 10402A = 3B = 4C = xA:B:C = 1/2:1/3:1/4= 6:4:36/13 * 1040= Rs.480Answer: D
Answer: D
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280 more at the second station it drops one half the new total and takes twelve more. On arriving at the third station it is found to have 250 passengers. Find the no of passengers in the beginning?
Options:
A)292
B)180
C)192
D)144
E)294
Rationale: Let no of passengers in the beginning be X
After first station no passengers=(X-X/3)+280=2X/3 +280
After second station no passengers =1/2(2X/3+280)+12
1/2(2X/3+280)+12=250
2X/3+280=2*238 = 476 - 280 = 196
2X/3=196
X=294. So the answer is option E) 294.
Answer: E
Question: A bag contains 5 green balls and 9 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Options:
A)11/21
B)17/42
C)23/42
D)46/91
E)51/91
Rationale: The total number of ways to draw two balls is 14C2 = 91
The number of ways to draw two green balls is 5C2 = 10
The number of ways to draw two white balls is 9C2 = 36
P(two balls of the same colour) = 46/91
The answer is D.
Answer: D
Question: In the xy-coordinate plane, the graph of y = -x^2 + 9 intersects line L at (p,5) and (t,7). What is the least possible value of the slope of line L?
Options:
A)6
B)2
C)-2
D)1
E)-10
Rationale: We need to find out the value of p and L to get to the slope.
Line L and Graph y intersect at point (p,5). hence, x= p and Y=5 should sactisfy the graph. soliving
5 = -p2 +9
p2 = 4
p = + or - 2
simillarly point (t,7) should satisfy the equation. hence x=t and Y=7.
-7 = -t2+9
t = +or - 4
considering p = -2 and t =4, the least slope is (7-5)/(4-2) = 1
IMO option D is correct answer.
Answer: D
Question: A wheel of a car of radius 21 cms is rotating at 800 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)39.6 km/hr
E)63.36 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 * 800 = 105600 cm in a minute.
In an hour, the wheel will cover a distance of 105600 * 60 = 6336000 cm.
Therefore, the speed of the car = 6336000 cm/hr = 63.36 km/hr
Choice E is the correct answer.
Answer: E
Question: {330, 380, 350, n}
Which of the following could be the median of the 4 integers listed above?
I. 340
II. 360
III. 380
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: If 340 is the median, (n+350) / 2 = 340. Then n = 330. Thus 340 can be the median.
If 360 is the median, (n+350) / 2 = 360. Then n = 370. Thus 360 can be the median.
If 380 is the median, (n+350) / 2 = 380. Then n = 410. But 410 > 380, which would then be the second largest member of the set, thus 380 can not be the median.
The answer is C.
Answer: C
Question: A certain team has 11 members, including Joey. A three-member relay team will be selected as follows: one of the 11 members is to be chosen at random to run first, one of the remaining 10 members is to be chosen at random to run second, and one of the remaining 9 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
Options:
A)1/1320
B)1/132
C)2/11
D)1/12
E)1/6
Rationale: Total outcomes= 11*10*9
Favorable Outcomes= 10*1*9 and 10*9*1
P=2*10*9*1/11*10*9
P=2/11
Ans C
Answer: C
Question: A sum of Rs.5000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)A)282
B)B)3250
C)C)8383
D)D)8383
E)E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 5000[1 + 10/100][1 + 20/100][1 + 25/100]
A = 5000 * 1.65
A = Rs.8250
So the interest = 8250 - 5000 = Rs.3250
Answer: B
Answer: B
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits T are in s(99)?
Options:
A)T=350
B)T=353
C)T=354
D)T=356
E)357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: B
Question: A, B, and C working alone can finish constructing a house in 6, 9, and 12 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
Options:
A)11:38 am
B)11:49 am
C)12:11 pm
D)12:32 pm
E)12:43 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/9 of the work each hour.
C completes 1/12 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 5/18 for a total of 8/18.
Working together, A, B, and C can complete 13/36 of the work each hour.
To complete 20/36, the time required is (20/36) / (13/36) = 20/13 hours.
The work will be completed at 12:00 plus 7*60/13 minutes which is about 12:32 pm.
The answer is D.
Answer: D
Question: It costs $5 for the first 1/3 hour to use the laundry machine at the Laundromat. After the first ¼ hour it costs $12 per hour. If a certain customer uses the laundry machine for 2 hours and 30 minutes, how much will it cost him?
Options:
A)$27.
B)$29.
C)$31.
D)$33.
E)$35.
Rationale: 2 hrs 30 min = 150 min
First 20 min ------> $5
Time left is 130 min...
Now, 60 min costs $ 12
1 min costs $ 12/60
150 min costs $ 12/60*130 => $ 26.00
So, Total cost will be $26 + $5 => $ 31
Hence answer will be C
Answer: C
Question: The C.P of 10 pens is equal to the S.P of 13 pens. Find his gain % or loss%?
Options:
A)loss 16 2/8%
B)loss 16 6/3%
C)loss 23.08%
D)loss 18 2/3%
E)loss 16 25%
Rationale: 10 CP = 13 SP
13 --- 3 CP loss
100 --- ? => 23.08% loss
Answer:C
Answer: C
Question: A boat moves upstream at the rate of 1 km in 40 minutes and down stream 1 km in 12 minutes. Then the speed of the current is :
Options:
A)1 kmph
B)2 kmph
C)1.75 kmph
D)2.5 kmph
E)3.5 kmph
Rationale: Rate upstream = (1/40 *60) = 1.5 kmph
Rate dowm stream = 1/12 * 60 = 5 kmph
Rate of the current = ½ (5-1.5) = 1.75 kmph
ANSWER:C
Answer: C
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 12, then v=
Options:
A)15
B)18
C)21
D)24
E)27
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
12 = 2v/3 - 2v/9 = 4v/9
v = 27
The answer is E.
Answer: E
Question: Lucia's sells kale at x dollar per pound for the first 20 pounds and .8x for every subsequent pound. Amby's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Lucia's becomes an equal or better deal?
Options:
A)24
B)26
C)25
D)27
E)28
Rationale: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
20x + (n-20) (0.8x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 20x + 0.8nx - 16x <= 14x + 0.9nx - 12.6x
==> 2.6x <=0.1nx
==> 26x < =nx
==> x (n-26) > = 0
as x cannot be 0,
==> n - 26 >=0
==> n > = 26
so the minimum value is 26
'B' would be the correct answer
Answer: B
Question: The average weight of 8 students decreases by 5 kg when one of them weighing 86 kg is replaced by a new student. The weight of the student is
Options:
A)46 kg
B)48 kg
C)70 kg
D)72 kg
E)None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 5 kg
=> (86-x)/8 = 5
=> x = 46
Answer : A
Answer: A
Question: If x = -1/8 and y = -1/2, what is the value of the expression -2x – y^2?
Options:
A)-3/2
B)-1
C)0
D)3/2
E)7/4
Rationale: -2X- y^2
-2x-1/8 - (-1/2)^2
1/4-1/4
0
C correct
Answer: C
Question: To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of L dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
Options:
A)L/T
B)L/(T-S)
C)SL/(T-S)
D)SL/T(T-S)
E)L(T-S)/T
Rationale: Since no absolute values are given in the question we can replace the given parameters with assumed numbers,
Let Total colleagues be 100 (T)
Let total contribution be 1000 (L) (point to note is that its total cost not per person)
Those who dont pay are S (30)
Per person cost = L/T = 1000/100 = 10
So cost for those who failed to pay = (L/T) * S = SL/T = 30*10=300
The equation for people who would bear the total cost after S people fail = (T-S)=70
There fore the solution is (SL/T)/ (T-S) = SL/T(T-S) = 300/70
Answer D
Hope this helps !!!
Answer: D
Question: 18 times a positive integer is more than its square by 80, then the positive integer is
Options:
A)13
B)10
C)11
D)12
E)14
Rationale: Explanation:
Let the number be x. Then,
18x = x2 + 80
=> x2 - 18x + 80 = 0
=>(x - 10)(x - 8) = 0
=> x = 10 or 8
Answer: B
Answer: B
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 25.6 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
Options:
A)15.1
B)15.4
C)15.7
D)16.0
E)16.3
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 25.6
x^2=2.56
x=1.6
At 4:00 pm, the amount of bacteria was 10(1.6)=16 grams.
The answer is D.
Answer: D
Question: The size of the wooden block is 5 x 10 x 20 cm .How many such blocks will be required to construct a solid wooden cube of minimum size?
Options:
A)6
B)8
C)12
D)16
E)18
Rationale: Explanation:
Side of smallest cube = L.C.M of 5,10,20 = 20cm
Volume of the cube = (20 x 20 x 20)cm3 = 8000 cm3
Volume of the block= (5 x 10 x 20) cm3 = 1000 cm3
Number of blocks = (8000/1000) = 8
Answer: B
Answer: B
Question: If the number 653 xy is divisible by 90, then (x + y) = ?
Options:
A)2
B)3
C)4
D)6
E)5
Rationale: 90 = 10 x 9
Clearly, 653xy is divisible by 10, so y = 0
Now, 653x0 is divisible by 9.
So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.
Hence, (x + y) = (4 + 0) = 4.
Answer: C
Answer: C
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052,3158, x
Options:
A)2643
B)5464
C)9476
D)7554
E)3158
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
11052 Ã— 3 + 2 = 3158
3158 Ã— 3 + 2 = 9476
C
Answer: C
Question: A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 3 : 2. Find how long B remained in the business?
Options:
A)5 months
B)8 months
C)6 months
D)7 months
E)None of these
Rationale: Initially A’s investment = 3x and B’s investment = 4x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 4x × n = 3 : 2
∴ 3x × 10 × 2 = 4x × n × 3
⇒ n = 5
Answer A
Answer: A
Question: An air conditioner can coo the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. if both air conditioners are switched on at same instance then how long will it take to cool the room?
Options:
A)about 22 minutes
B)about 20 minutes
C)about 30 minutes
D)about 25 minutes
E)about 15 minutes
Rationale: Take LCM of 40 and 45 = 360
40*9=360 / 45*8=360.
So if both are switched on together , room cooled in 360/(8+9)=360/17=21.16 minutes
21.16 can be round to 22 minutes , so about 22 minutes
ANSWER:A
Answer: A
Question: A rope of which a calf is tied is increased from 12 m to 25 m, how much additional grassy ground shall it graze?
Options:
A)1217
B)1219
C)1511.7
D)1212
E)1312
Rationale: π (252 – 122) = 1511.7
Answer:C
Answer: C
Question: The average temperature of the town in the first four days of a month was 56 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Options:
A)62 degrees
B)64 degrees
C)65 degrees
D)128 degrees
E)67 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (56 * 4) = 224 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 16 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 16 or x = 16. Answer: D
Temperature on the 5th day = 8x = 128 degrees.
Answer: D
Question: There was two trains from calcutta to kanyakumari one train is fast service travels with a speed 75km per hour another travels with a speed of 44km per hour the time taken to reach from calcutta to kanyakumari is 4hours less than the first train...find the distance b/w calcatta to kanyakumari
Options:
A)415.8 km
B)425.8 km
C)435.8 km
D)445.8 km
E)455.8 km
Rationale: let distance b/w calcutta to kanyakumari is = x km
then eqn is
x/44 - x/75 = 4
=> x*(75-44)=4*75*44
=> x = 425.8 km
ANSWER:B
Answer: B
Question: The arithmetic mean and standard deviation of a certain normal distribution are 16.2 and 2.3, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)10.5
B)11
C)11.6
D)12
E)12.5
Rationale: Mean = 16.2
Two standard deviations is 2.3 + 2.3 = 4.6
There could be two calues for this.
Mean + two standard deviations = 20.8
Mean - Two standard deviations = 11.6
Answer choice has 11.6 and so C is the answer.
Answer: C
Question: If 4a = 16b and 9b = 11c, Find a:b:c?
Options:
A)52:13:7
B)44:11:9
C)7:13:52
D)7:13:54
E)None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 11c ==> b/c = 11/9)
==> a:b = 16:4 and b:c = 11:9
a:b:c = 44:11:9
Answer: Option B
Answer: B
Question: A wooden cube whose edge length is 8 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
Options:
A)46.3%
B)50.4%
C)54.2%
D)57.8%
E)61.3%
Rationale: There are a total of 8*8*8 = 512 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 6*6*6 = 216 cubes.
The number of cubes with at least one side painted red is 512 - 216 = 296 cubes
The probability that a cube has at least one side painted red is 296/512 which is about 57.8%
The answer is D.
Answer: D
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 39 kms in 3 hrs. In what time would it cover the same distance upstream?
Options:
A)3.5 hours
B)6 hours
C)4 hours
D)5 hours
E)6 hours
Rationale: Still Water=12km/hr
Downstream=39/3=13km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+13/2 = 11km/hr
So time taken in upstream = 39/11 =3.5hrs
ANSWER:A
Answer: A
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Options:
A)11 1/5
B)11 1/4
C)11 1/5
D)11 1/3
E)11 2/3
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Answer: B
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)5
B)8
C)7
D)4
E)2
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Options:
A)27.5%
B)37.5%
C)47.5%
D)57.5%
E)67.5%
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
ANSWER:B
Answer: B
Question: If a certain sample of data has a mean of 20.0 and a standard deviation of 5.0, 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) 23.5
E) 26.5
Rationale: The standard deviation is 5. 2.5 standard deviations, which is just 2.5 x 5.0 is 12.5. The only answer more than 12.5 away from the mean is B.
Answer: B
Question: A store’s selling price of $2240 for a certain computer would yield a profit of 40 percent of the store’s cost for the computer. What selling price would yield a profit of 50 percent of the computer’s cost?
Options:
A)$2400
B)$2464
C)$2650
D)$2732
E)$2800
Rationale: 2240 = X * 1.4 = X * (7/5). Therefore, X = 2240 * 5/7.
2240 is easily divided by 7 to be 320, which is then easily multiplied by 5 to give X = 1600. To get 50% profit, you need 1600 * 1.5 = 2400.
Answer: A
Answer: A