divelab/Sys2Bench huggingface dataset:
Question: Potatoes are made up of 99% water and 1% potato matter. Jack bought 100 pounds of potatoes and left them outside in the sun for a while. When he returned, he discovered that the potatoes had dehydrated and were now only made up of 98% water. How much did the potatoes now weigh?
Options:
A)50 lb
B)80 pounds
C)90 pounds
D)100 pounds
E)60 pounds
Rationale: initially water weigh 99 pounds & patato matter weigh 1 pound.
after dehydration
water = 98%
=> potato matter = 2% = 1 pound
100% = (1/2) * 100 = 50 pounds
So, potato now weigh 50 pounds.
ANSWER:A
Answer: A
Question: A room of 6m 20cm long and 5m 74cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Options:
A)88900
B)87700
C)88970
D)88000
E)89000
Rationale: Explanation:
area of the room = 620 * 574 sq cm
size of largest square tile = H.C.F of 620cm and 574cm= 2cm
area of 1 tile = 2*2 sq cm
no. of tiles required = (620*574) / (2* 2) = 88970
Answer: C) 88970
Answer: C
Question: John has 5 flavors of chocolate in him shop. How many options are there for Jones to pick a one-flavor, two-flavor, three-flavor, four-flavor or five-flavor order?
Options:
A)22
B)31
C)43
D)37
E)38
Rationale: 5C1 + 5C2+ 5C3+5C4+5C5 = 31.
Answer: B
Answer: B
Question: A movie buff owns movies on DVD and on Blu-ray in a ratio of 7:2. If she buys 5 more Blu-ray movies, that ratio would change to 13:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?
Options:
A)22
B)28
C)77
D)99
E)351
Rationale: if u can just keep an eye on the options
99 is the only multiple of 9 in options given .. SO you can mark it wid in seconds.
Now coming to the process m(D) = 7x and b(D) = 2x
now from the next line the new eqn becomes 7x/ (2x + 6) = 13/4
Solving it 28x = 26x + 78
x =39
which means m (d) = 273 and b(d) = 78
SO total initially is m(d) + b(d) = 351
E
Answer: E
Question: A car covers a distance of 630 km in 6 ½ hours. Find its speed?
Options:
A)105 kmph
B)176 kmph
C)298 kmph
D)186 kmph
E)268 kmph
Rationale: 630/6
= 105 kmph
Answer:A
Answer: A
Question: What will be the compound interest on Rs. 35000 after 3 years at the rate of 12 % per annum
Options:
A)Rs 13123.20
B)Rs 14103.48
C)Rs 12172.48
D)Rs 14172.48
E)None of these
Rationale: Explanation:
(35000×(1+12/100)3)
=>35000×28/25×28/25×28/25
=>49172.48
So Compound interest will be 49172.48 - 35000
= Rs 14172.48
Option D
Answer: D
Question: If X boxes of mango juice cost 250 cents, how much will Y boxes cost in dollars?
Options:
A)Y*2/x
B)Y*2.6/x
C)2Y*2.5/x
D)Y*2.5/x
E)3Y*2.5/x
Rationale: X boxes of mango juice cost 250 cents or 2.5 dollars.
cost of mango juice = 2.5/x
Cost of Y mango juices = Y*2.5/x
Hence Answer : D
Answer: D
Question: root X+3=X root X+3 how many solution???
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: root(x+3)=x root(x+3)
=>square both side
=>x+3=x2(x+3)
=>(x+3)(x2-1)
=>(x+3)(x+1)(x-1)
hence 3 solution is there
ANSWER:C
Answer: C
Question: If xy=25, x/y=36, for positive numbers x and y, y=?
Options:
A)1/2
B)2
C)1/3
D)3
E)5/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=25 ---> x=25/y - (i)
x/y=36 ---> replacing (i) here ---> 25/(y^2)=36 ---> y^2=25/36---> y=5/6 or -5/6
The question states that x and y are positive integers. Therefore, y=5/6 is the answer.
Answer E.
Answer: E
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)10
B)12
C)14
D)16
E)19
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: Five kids were sharing out a box of candies. Amar took one-third, Babu took one-quarter,Chetan took one-fifth, and Dinakar took one-sixth. That left six candies as Shiva's share. Howmany candies were altogether?
Options:
A)100
B)120
C)140
D)160
E)180
Rationale: let the total no of candies in a box= x
then aman took=x/3
babu took=x/4 and chetan took = x/5 and the remaining should be shiva's share
then
x-(x/3+x/4+x/5+x/6) =6 i.e 3x/60=6
therefore x=120
ANSWER:B
Answer: B
Question: Suresh borrowed some money at the rate of 12% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
Options:
A)s.8500
B)s.6000
C)s.6800
D)s.9000
E)s.7000
Rationale: using the formula S.I=P*T*R/100
(x*12*3/100)+(x*9*5/100)+(x*13*3/100)=8160
x=6800
i.e money borrowed is Rs.6800
ANSWER:C
Answer: C
Question: a batmans runs just before the last match of the season adds up750 in his last two innings his scores only 6 scores and his avg drop by 2 fond his final avg of the season?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Formula for this question is
6 = 2*avg-2(N+2)
6 = 2*(750/n) - 2(n+2)
n*n+5n-750 = 0
n= 25
so final ans 23
ANSWER:C
Answer: C
Question: What is the sum of the different positive prime factors of 880?
Options:
A)5
B)10
C)15
D)18
E)21
Rationale: Prime factorization of 880
=88 * 10
=8*11 * 10
=2*4 * 2*5 * 11
=2* 2*2 * 2*5 * 11
=2^4 * 5 * 11
Sum of the different positive prime factors of 880 = 2+5+11
=18
Answer D
Answer: D
Question: There are two positive numbers in the ratio 7:11. If the larger number exceeds the smaller by 16, then find the smaller number?
Options:
A)25
B)26
C)30
D)24
E)28
Rationale: Let the two positive numbers be 7x and 11x respectively.
11x - 7x = 16
4x = 16 => x = 4
=> Smaller number = 7x = 28.
Answer: E
Answer: E
Question: If x is divisible by 3 and 4, which of the following must divide evenly into x?
I. 2
II. 38
III. 41
Options:
A)I only
B)I and II
C)II​ and III
D)II​ only
E)I, II, and III
Rationale: If x is divisible by 3,4 means it will be = or > 12, 24,48 etc...
That are not divisible by 38, 41.
So, the answer is A
Answer: A
Question: X can give Y 100 meters start and Z 200 meters start in X kilometer race. How much start can Y give Z in X kilometer race?
Options:
A)112.2m
B)216.3m
C)111.12m
D)213.27m
E)222.40m
Rationale: C
111.12 m
X runs 1000 m while Y runs 900 m and Z runs 800 m.
The number of meters that Z runs when Y runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
Y can give Z = 1000 - 888.88 = 111.12 m.
Answer: C
Question: Find the smallest number of 6 digits which is exactly divisible by 111.
Options:
A)100011
B)111111
C)101111
D)201111
E)211111
Rationale: Smallest number of 6 digits is 100000.
On dividing 100000 by 111, we get 100 as remainder.
Number to be added = (111 - 100) - 11.
Hence, required number = 100011
Option A
Answer: A
Question: What is the product of all the possible values of x if x^2+5x+6?
Options:
A)12
B)18
C)15
D)6
E)9
Rationale: Explanation:
=> y= x^2+5x+6
=> y= (x+2) (x+3)
=> x= -2, x= -3
Product x = (-2)(-3) = 6
answer option 6
ANSWER:D
Answer: D
Question: A goods bullet train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 seconds. What is the length of the goods bullet train?
Options:
A)220m
B)250m
C)280m
D)210m
E)270m
Rationale: E
270m
Answer: E
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive
Options:
A)233
B)381
C)900
D)287
E)271
Rationale: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (4650 * 6/31) = Rs, 900.
Answer: C) Rs.900
Answer: C
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)21 ½ days
B)22 ½ days
C)23 ½ days
D)12 ½ days
E)None of these
Rationale: Explanation:
1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2 = 22 ½ days
Answer: B
Answer: B
Question: the average weight of four pigs is 15 kg.weight less than 16 kg is considered as under weight.what maximum no. of pig can be under weight.
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: sum of all four pigs weigh=60kg
it is possible that all four pigs are underweight.
because the average is 15kg which itself underweight.
answer E
Answer: E
Question: Which of the following must be non-negative?
Options:
A)(a-0.9)(a-1)
B)(a+1)(a-1)
C)(a+0.9)(a+1)
D)(a-0.9)(a-0.9)
E)a(a+1)
Rationale: a^2+a
f'(a)=2a+1=0 => a=-1/2
f''(a) =2>0 => a= -1/2 is point of minima Putting this value in main equation we get -1/2 (-ve)
Option D
F(a)=(a - 0.9)^2
f'(a)= 2(a-0.9)=0 => a=0.9
f''(a)= 2>0 => a= 0.9 is point of minima. Putting in main equation we get 0 which is non negative.
Answer: D
Answer: D
Question: There are 10 baskets numbered from 1 to 10 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
Options:
A)330
B)390
C)450
D)510
E)570
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8+9+10 = 10*11/2 = 55 apples.
The total number of apples taken by 10 children is 10*55 = 550
The number of apples left in the end is 1000 - 550 = 450 apples.
The answer is C.
Answer: C
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
Options:
A)9 kmph
B)10 kmph
C)12 kmph
D)14 kmph
E)16 kmph
Rationale: Let the distance travelled by x km.
Then, x - x = 2
10 15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60 kmph. = 12 kmph.
5
C
Answer: C
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?
Options:
A)10
B)12
C)8
D)15
E)16
Rationale: Explanation :
Let the required hours needed be x
More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)
⇒3 × 2 × 8 = 4 × 1 × x
⇒ 3 × 2 × 2 = x
⇒ x = 12 . Answer : Option B
Answer: B
Question: If n > 0 , which of the following must be true?
I n^2 < 1
II	n - n^2 < 0
III	2n - 1 < 0
Options:
A)I only
B)II only
C)III only
D)I and II only
E)none
Rationale: I. False for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	False for all values of n
Hence the correct answer will be (B)
Answer: B
Question: A certain junior class has 1000 students and a certain senior class has 900 students. Among these students, there are 60 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
Options:
A)3/40000
B)2/30000
C)9/2000
D)1/60
E)1/15
Rationale: Let's see
Pick 60/1000 first
Then we can only pick 1 other pair from the 800
So total will be 60 / 900 *1000
Simplify and you get 2/30000
Answer is B
Answer: B
Question: What is the probability that Company E's advertisement will be one of the first two be shown during the first commercial break?
Options:
A) 1/ 225
B) 1 / 30
C) 1 /15
D) 2 / 15
E) 4 /15
Rationale: E 1/15 + (14/15) * 1/14 = 2/15 D
Answer: D
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Options:
A)11%
B)11 2/9%
C)11 1/9%
D)10%
E)9%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
ANSWER:C
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, ?, 1
Options:
A)1
B)2
C)5
D)7
E)9
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
B
Answer: B
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?
Options:
A)5 months
B)6 months
C)7 months
D)8 months
E)4 months
Rationale: Bankers Discount, BD = Simple Interest on the face value of the bill for unexpired time.
True Discount, TD = Simple Interest on the present value for unexpired time.
Simple Interest on Rs. 1600 = True Discount on Rs.1680
=> Rs. 1600 is the Present Worth (PW) of Rs. 1680
=> Rs. 80 is the Simple Interest of Rs.1600 at 15%
⇒80=(1600×T×15)/100
⇒80=16×T×15
⇒5=T×15
⇒1=T×3
⇒T=1/3 year
=12/3 months
=4 months
ANSWER:E
Answer: E
Question: When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 8x is divided by 9?
Options:
A)0
B)1
C)3
D)4
E)6
Rationale: i tried plugging in numbers
x = 9q+5
x = 14
8x = 112
8x/9= 9*12+4
remainder is 4.
Answer is D.
Answer: D
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
Options:
A)128
B)131
C)132
D)143
E)145
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: Pipe A can fill a tank in 10 hours. Due to a leak at the bottom, it takes 15 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)76
B)84
C)56
D)75
E)30
Rationale: Let the leak can empty the full tank in x hours 1/10 - 1/x = 1/15
=> 1/x = 1/10 - 1/15 = (3 - 2)/30 = 1/30
=> x = 30.
Answer: E
Answer: E
Question: If 4 men can reap 40 acres of land in 15 days, how many acres of land can 16 men reap in 30 days?
Options:
A)320
B)240
C)369
D)489
E)125
Rationale: 4 men 40 acres 15 days
16 men ? 30 days
40 * 16/4 * 30/15
40 * 4 * 2
40 * 8 = 320
Answer:A
Answer: A
Question: Excluding stoppages, the speed of a bus is 48 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)5
B)4.15
C)4.25
D)5.5
E)None of these
Rationale: Due to stoppages, it covers 314 km less.
Time taken to cover 3 km = ((3/48)Ã—60) =4.15 min.
Option(B) is correct
Answer: B
Question: A retailer bought a machine at a wholesale price of $117 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?
Options:
A)81
B)100
C)120
D)135
E)159
Rationale: My solution: Wholesale Price= 117
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 117+ 1/5(117)
x=156;
ANSWER:E
Answer: E
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 10% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
Options:
A)$15,840
B)$17,820
C)$18,000
D)$19,800
E)$18,810
Rationale: 10000 seats --> Full Price : Half Price = 9000 : 1000
Price when all seats are filled = 18000 + 1000 = 19000
100 seats are unsold --> Loss due to unfilled seats = 10 + 2*90 = 190
Revenue = 19000 - 190 = 18810
Answer: E
Answer: E
Question: The denominator of a fraction is 15 greater than the numerator. If the numerator and the denominator are increased by 3, the resulting fraction is equal to 3â„4. What is the value of the original fraction?
Options:
A)23/38
B)29/44
C)33/48
D)38/53
E)42/57
Rationale: Let the numerator be x.
Then the denominator is x+15.
x+3 / x+18 = 3/4.
4x+12=3x+54.
x=42.
The original fraction is 42/57.
The answer is E.
Answer: E
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)12
B)42
C)62
D)20
E)87
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: D
Answer: D
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
Options:
A)45 kg
B)50 kg
C)53 kg
D)55 kg
E)None
Rationale: Solution
Weight of the teacher	= (35.4 x 25 - 35 24)kg
= 45 kg
Answer A
Answer: A
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1700. The difference between the profit shares of A and C is?
Options:
A)288
B)266
C)155
D)680
E)441
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1700
=> 5 parts out of 15 parts is Rs. 1700
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1700) = Rs. 680
Answer:D
Answer: D
Question: A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B's contribution in the capital is
Options:
A)7000
B)8000
C)9000
D)10000
E)None of these
Rationale: Explanation :
Ratio in which profit is divided = 2:3
Assume that B's contribution to the capital = b
=> 3500*12 : b*7 = 2:3
=> 3500*12/7b = 2/3
=> b = (3500*12*3)/(2*7) = 500*6*3 = 9000. Answer : Option C
Answer: C
Question: How much is 80% of 40 is greater than 4/5 of 15?
Options:
A)12
B)20
C)18
D)12
E)81
Rationale: (80/100) * 40 â€“ (4/5) * 15
32 - 12 = 20
Answer:B
Answer: B
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 3?
Options:
A)1/8.
B)1/2.
C)1/5.
D)3/8.
E)1/3.
Rationale: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 1/8. Option A.
Answer: A
Question: An inspector rejects 0.06% of the meters as defective. How many will he examine to reject 2?
Options:
A)A)1500
B)B)2000
C)C)2500
D)D)3000
E)E)3333
Rationale: Let the number of meters to be examined be x
Then, 0.06% of x = 2
(6/100)*((1/100)*x = 2
x = 3333
Answer is E
Answer: E
Question: A boat running upstream takes 640 min to cover a certain distance, while it takes 280 min to cover the same distance running down stream. What is the ratio between the speed of the boat and speed of water current respectively?
Options:
A)23: 7
B)22: 9
C)23: 8
D)23: 9
E)23: 11
Rationale: Let the speed of the boat=x and speed of the current=y
Relative speed in upstream=x-y and in downstream=x+y
Let the distance 'd' is to be covered in downstream and upstream, then
Time taken in upstream=d/(x-y)=640 or d=640(x-y) ----(i) and
Time taken in downstream=d/(x+y)=280 or d=280(x+y) ----(ii)
Comparing (i) & (ii), 640(x-y) = 280(x+y)
=> 16(x-y) = 7(x+y)
=> 16x -16y =7x -7y
=> 9x = 23y
=> x/y= 23/9
ANSWER:D
Answer: D
Question: A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 78 runs, thereby increasing his average by 6 runs. His new average is
Options:
A)18 runs
B)28 runs
C)48 runs
D)42 runs
E)46 runs
Rationale: Explanation:
Let average for 10 innings be x. Then,
(10x + 78)/11 = x + 6 => 11x + 66 = 10x + 78 => x = 12.
New average = (x + 6) = 18 runs.
Answer: A
Answer: A
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^90?
Options:
A)180
B)160
C)140
D)150
E)120
Rationale: Put in simple words, we need to find the highest power of 2 in 100^90
100 = 2^2*5^2
Therefore 100^90 = (2^2*5^2)^90 = 2^180*5^180
Answer : A
Answer: A
Question: For dinner, Cara ate 240 grams of bread which was eight times as much bread as she ate for lunch, and six times as much bread as she ate for breakfast. How much bread did Cara eat in total?
Options:
A)300
B)310
C)320
D)330
E)340
Rationale: For breakfast, Cara ate 240 / 6 = 40 grams.
For lunch, Cara ate 240 / 8 = 30 grams.
For dinner, Cara ate 240 grams.
The total is 40 + 30 + 240 = 310 grams.
The answer is B.
Answer: B
Question: Solution X contains 20% of material A and 80% of material B. Solution Y contains 30% of material A and 70% of material B. A mixture of both these solutions contains 22% of material A in the final product. how much solution X is present in the mixture?
Options:
A)40%
B)60%
C)80%
D)100%
E)110%
Rationale: We can assume the total weight of the mixture= 100
Conc of A in the final mixture= 22
Let weight of A in the mixture be X. Conc given= 20%=.2
Therefore, weight of B= 100-X. Conc given = 30%= .3
Now, acc to the problem, .2X+ .3(100-X)=22
Solving, we get X=80. Since we assumed the weight of the mixture = 100, Therefore presence of A in the mixture= 80%.
ANSWER:C
Answer: C
Question: A number of two digits has 3 for its unit’s digit, and the sum of digits is 1/7 of the number itself. The number is
Options:
A)43
B)63
C)73
D)53
E)83
Rationale: Let the ten’s digit be x.
Then, number=10x+3 and sum of digits=(x+3)
(x+3)=1/7(10x+3)
7x+21=10x+3
3x=18
X=6
The required number is 63
ANSWER B 63
Answer: B
Question: A can do a job in 5 days and B can do it in 15 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)21 ½ days
B)22 ½ days
C)23 ½ days
D)12 ½ days
E)7 ½ days
Rationale: Explanation:
1/5 + 1/15 = 4/15 = 4/15
15/4 = 15/4 *2 = 7 ½ days
Answer: E
Answer: E
Question: Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°.
If the number of convex corners in such a polygon is 25, the number of concave corners must be
Options:
A)20
B)10
C)21
D)22
E)23
Rationale: 90(25) + 270(n-25) = (n-2)*180.
=25 + 3(n-25) = (n-2)*2.
= 3n - 50 = 2n-4
= n = 46.
Hence, the required number of corners must be 46 - 25 = 21. ANSWER : C
Answer: C
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.4
C)1.1
D)1.5
E)1.2
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: D
Question: For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
Options:
A)10
B)9
C)8
D)7
E)6
Rationale: "For any positive integer n , n > 1, the "length" of n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)"
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 9 the length of 512.
the answer is (B)
Answer: B
Question: A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: X PIPES FILL AND 8-X EMPTY
IN 1hr 1/6th is emptied so :
x/6 - (8-x)/8 = 1/6
ON SOLVING X=4 (FILL PIPES) AND 8-X=4(EMPTY PIPES)
ANSWER:D
Answer: D
Question: The number 49 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
Options:
A)11
B)16
C)15
D)14
E)13
Rationale: I think brute force with some common sense should be used to solve this problem.
Write down all perfect squares less than 49: 1, 4, 9, 16, 25, 36, 49..
Now, 49 should be the sum of 3 of those 7 numbers. Also to simplify a little bit trial and error, we can notice that as 49 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd).
We can find that 49 equals to 4+9+36=2^2+3^2+6^2=49 --> 2+3+6=11.
Answer: A.
Answer: A
Question: From the set of numbers {t, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
Options:
A)8
B)15
C)16
D)31
E)32
Rationale: Any letter (v, w, x, y, z) can be included or not.
Thus there are 2^5 combinations - 1 empty combination = 31 combinations
The answer is D.
Answer: D