mathewhe/aqua_rat huggingface dataset:
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @Rs.26.50 per metre is Rs.5300, what is the length of the plot in metres?
(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
Rationale: Length of the fence =530026.50=200 m
⇒ 2(length + breadth)=200 m
⇒ 2(breadth + 20 + breadth)=200 m (∵ length = breadth+20)
⇒ breadth + 20 + breadth =100 m
⇒ breadth =40 m
length =40+20=60 m
Answer is B.
Answer: (B) 60
Question: A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, " How many gold coins do we have?" After a brief pause, he replied, "Well! if I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins the merchant has?
(A) 96
(B) 53
(C) 43
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let the numbers of gold coins = x + y
=> 48(x-y) = x2 - y2.
=> 48(x-y) = (x- y)(x + y).
=> x + y = 48.
Answer : D
Answer: (D) None of these
Question: How many days are there in x weeks x days
(A) 14x
(B) 8x
(C) 7x^2
(D) 7
(E) 6
Rationale: Explanation:
x weeks x days =(7×x)+x = 7 x+x=8x days
Answer: Option B
Answer: (B) 8x
Question: How many two-element subsets of {6,7,8,9} are there that do not contain the pair of elements 8 and 9?
(A) 5
(B) 4
(C) 3
(D) 6
(E) 7
Rationale: Required subsets are = {6,7}, {6,8}, {6,9}, {7,8}, {7,9} = 5
Answer: A
Answer: (A) 5
Question: A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?
(A) A)23
(B) B)33
(C) C)43
(D) D)53
(E) E)63
Rationale: 43.
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9). answer is C
Answer: (C) C)43
Question: The positive integer b is divisible by 5.
What is the remainder when dividing 3(6+b)(5+b) by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When we multiply any of these options: 3*11*10 (b=5) or 3*16*15 (b=10) we end up with numbers ending in 0 which are exactly divisible by 5 leaving no remainder.
Hence answer is A.
Answer: (A) 0
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 288
(C) 276
(D) 188
(E) 112
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: (A) 250
Question: Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: work done by A => 18/24
work done by B => x/32
18/24 + x/32 = 1
3/4 + x/32=1
24+x=32 => x=8
after 8 min b should be closed
ANSWER:C
Answer: (C) 8
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
(A) 3% decrease
(B) 5% decrease
(C) 9% decrease
(D) 8% decrease
(E) 6% decrease
Rationale: (30 * 30)/100
= 9% decrease
Answer: C
Answer: (C) 9% decrease
Question: The ratio of three numbers is 1:2:4 and the sum of their squares is 4725. The sum of the numbers is?
(A) A)10
(B) B)12
(C) C)15
(D) D)14
(E) E)9
Rationale: Let the numbers be x,2x,4x
then, x^2+4x^2+16x^2 = 4725
21x^2 = 4725
x^2 = 225
x=15
Answer is C
Answer: (C) C)15
Question: Which number is the odd one out?
9654 4832 5945 7642 7963 8216 3649
(A) 4950
(B) 2223
(C) 2292
(D) 3928
(E) 3649
Rationale: E
3649
In all the others multiply the first two digits together to produce the number formed by the last two digits.
Answer: (E) 3649
Question: One fourth of a solution that was 10% sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.
Answer: A.
Answer: (A) 34%
Question: Tough and Tricky questions: Word Problems.
Mike, Sarah and David decided to club together to buy a present. Each of them gave equal amount of money. Luckily Sarah negotiated a 20% discount for the present so that each of them paid 4 dollars less. How much did they pay for a present?
(A) 20
(B) 36
(C) 48
(D) 60
(E) 72
Rationale: Answer C.
We know that Sarah negotiated a discount of 20%, so each of them paid $4 less. Since there are three people, the 20% of the original price amounts to $12. 5 times 12$ is 60$, so the original price, before Sarah negotiated the discount, had been $60. They paid $12 less than the base price, so they spent $48.
Answer: (C) 48
Question: Sudhir started a business with Rs.40,000 and after 8 months Ravi joined him with Rs.60,000. If they get a profit of Rs.28000 then ratio of their shares will be
(A) 3:2
(B) 2:1
(C) 4:3
(D) 3:4
(E) 3:5
Rationale: 40000*12:60000*(12-8)
=480000 :240000
=2:1
ANSWER:B
Answer: (B) 2:1
Question: The area of a triangle is with base 5.5m and height 6m?
(A) 11 m2
(B) 16.5 m2
(C) 18.5 m2
(D) 19.5 m2
(E) 12 m2
Rationale: 1/2 * 5.5* 6
= 16.5 m2
Answer: B
Answer: (B) 16.5 m2
Question: From the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n is odd
(C) n is even
(D) n*n is even
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: Two trains of length 100 meters and 200 meters are 840 meters apart. They are moving towards each other on parallel tracks, at speeds of 54 km/h and 72 km/h. After how many seconds will the trains meet?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: The speeds are 54000/3600 = 15 m/s and 72000/3600 = 20 m/s
The relative speed is 35 m/s.
time = 840 / 35 = 24 seconds
The answer is C.
Answer: (C) 24
Question: How many three-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Required subsets are = {1,2,3}, {1,3,4}= 2
Answer: B
Answer: (B) 2
Question: If a(a + 6) = 27 and b(b + 6) = 27, where a ≠ b, then a + b =
(A)  −48
(B)  −6
(C)  2
(D)  46
(E)  48
Rationale: a(a + 6) = 27 and b(b + 6) = 27
=> a, b must be integers and if a is -9 or 3, b will be 3 and -9 respectively
=> a+b = -6
Ans: B
Answer: (B)  −6
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 65 seconds
(B) 46 seconds
(C) 40 seconds
(D) 97 seconds
(E) 26 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25)
= 40 seconds
Answer:C
Answer: (C) 40 seconds
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 1 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 120
(C) 289
(D) 270
(E) 927
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 1 = 120
Answer: B
Answer: (B) 120
Question: A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, 4, and 5, how many palindromes are possible?
(A) 25
(B) 75
(C) 125
(D) 225
(E) 625
Rationale: There are 5 choices for each of the first three digits.
The number of possible palindromes is 5^3=125.
The answer is C.
Answer: (C) 125
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 2.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
(A) (320 - y)/(5x)
(B) (y +250)/(5x)
(C) 5(80 - y)/(4x)
(D) (y + 400)/(4x)
(E) (4y + 250)/(5x)
Rationale: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 2.25 x => 2.25 * 20 = 45 houses per week
total time they took = (40/20) + (40/45) = 2.9 weeks
Putting the values of x and y in equation B
(y +250)/(5x) = (40+250)/5*20 = 290/100 = 2.9
Answer: (B) (y +250)/(5x)
Question: You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
(A) 180
(B) 181
(C) 182
(D) 178
(E) 168
Rationale: add the max weights
52+50+78=180
ANSWER:A
Answer: (A) 180
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $46,875, how much profit did the business make?
(A) $55,000
(B) $75,000
(C) $95,000
(D) $115,000
(E) $125,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 46875
P = $75,000
The answer is B.
Answer: (B) $75,000
Question: When the price of an article was reduced by 40% its sale increased by 80%. What was the net effect on the sale?
(A) 8% increase
(B) 4% decrease
(C) 6% increase
(D) 66% increase
(E) 66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 40%, the new price is 0.6p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.6p)(1.8n) = 1.08np, which is 1.08 times the old revenue, so is 8% greater.
ANSWER:A
Answer: (A) 8% increase
Question: If (20)² is subtracted from the square of a number, the answer so obtained is 4321. What is the number?
(A) 68
(B) 69
(C) 70
(D) 71
(E) 72
Rationale: x^2=4321+400=4721
4761=69*69
x=69
ANSWER:B
Answer: (B) 69
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1245
(B) 1268
(C) 1290
(D) 1345
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability T this college graduate has a graduate degree?
(A) 1/11
(B) 1/12
(C) 1/13
(D) 3/19
(E) 3/43
Rationale: In believe the answer is D. Please see below for explanation.
0) we are told the following ratios
CGD - College Graduate with Degree
NCG - Non College Graduate
CGN - College Graduate no Degree
CGD NCG CGN
1 8
3 2
In order to make CGD and CGN comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get
CGD NCG CGN
3 24 16
If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?
Nr of CGD = 3
Nr of CG = 3+ 16 = 19
Probability T of CGD / (CG) -> 3/19
Answer D
Answer: (D) 3/19
Question: The greatest common factor of positive integers m and n is 14. What is the greatest common factor of (2m^2, 2n^2)?
(A) 14
(B) 28
(C) 196
(D) 392
(E) 784
Rationale: m = 14j and n = 14k, where the greatest common factor of j and k is 1.
2m^2 = 2*14*14*j^2 and 2n^2 = 2*14*14*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*14*14 = 392
The answer is D.
Answer: (D) 392
Question: A sun is divided among X, Y and Z in such a way that for each 5 rupees X gets, Y gets 3 rupees and Z gets 2 rupees. If the share of Z is RS. 200, what is the total amount of X and Y?
(A) 650
(B) 800
(C) 600
(D) 700
(E) 900
Rationale: x:y:z = 500:300200
5:3:2
2 --- 200
8 --- ? => 800
Answer: B
Answer: (B) 800
Question: If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 2
II. 1
III. -2
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.
n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.
It can be 1 for n=2 and 2 for n=5.
Answer: C.
Answer: (C) I and II only
Question: If xy > 0, 1/x + 1/y = 15, and 1/xy = 5, then (x+y)/5 = ?
(A) 1/25
(B) 1/6
(C) 3/5
(D) 5
(E) 6
Rationale: (1/X+1/Y)=15 canbe solved as {(x+y)/xy}=5. Substituting for 1/xy=5, we get
x+y=15/5
==> (x+y)/5= 15/(5*5)=3/5.
C
Answer: (C) 3/5
Question: A farmer sells his strawberries through a distributor, which take a commission of 12% of the price set by the farmer. The distributor obtains the product from a farmer at the price of $35 per bushel. What is the price that the buyer observers if the distributor wants to maintain a 12% profit on the cost of a bushel?
(A) 66.22
(B) 44.55
(C) 44.05
(D) 66.02
(E) 75.48
Rationale: Farmer price = $35;The distributor wants to maintain a 12% profit on the cost of each strawberry bushel, thus he must get $35*1.12 = $39.20 after the distributor takes a commission of 12% of the final price --> (final price)*0.88 = $39.20 --> (final price) = $44.55Answer: B.
Answer: (B) 44.55
Question: A train passes a man standing on the platform. If the train is 160 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 5 sec
(B) 6 sec
(C) 8 sec
(D) 9 sec
(E) 7 sec
Rationale: D = 160
S = 72 * 5/18 = 20 mps
T = 160/20 = 8 sec
ANSWER:C
Answer: (C) 8 sec
Question: Length of a rectangular plot is 12 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 56 m
(B) 60 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let breadth = x metres.
Then, length = (x + 12) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 12) + x] = 200
2x + 12 = 100
2x = 88
x = 44
Hence, length = x + 12 = 56 m
A
Answer: (A) 56 m
Question: How much time does a train 125 metres long running at 60 km/hr take to pass a pole?
(A) 7.9s
(B) 2.5s
(C) 7.5s
(D) 7.6s
(E) 7.4s
Rationale: Explanation:
60 km/hr = 60 * 5/18 = 16.67 m/s
Speed = distance/time; v = d/t
16.67 = 125/t
t = 7.5s
ANSWER: C
Answer: (C) 7.5s
Question: A car travels uphill at 30 km/hr and downhill at 90 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
(A) 32kmph
(B) 39kmph
(C) 34kmph
(D) 35kmph
(E) 36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/90=5/9;
avg speed=150/(10/3+5/9)=39kmph
ANSWER:B
Answer: (B) 39kmph
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction R of the total distance did he cover while the sun was shining on him?
(A) 1/4
(B) 4/5
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is R=2/14 = 1/7. Answer: E
Answer: (E) 1/7
Question: 4,25,49,121,169,289,361,
(A) 149
(B) 169
(C) 189
(D) 529
(E) 219
Rationale: 23^2= 529 because follow sequence of square of the prime numbers
ANSWER:D
Answer: (D) 529
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
(A) 31
(B) 66
(C) 55
(D) 77
(E) 81
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 = 31.
Answer: A
Answer: (A) 31
Question: Two men and three women can repair a bridge in 10 days while three men and two women can do same work in 8 days. If two men and one woman are used to finish this work, in how many days they will complete it?
(A) 9.7 days
(B) 12.5 days
(C) 10 days
(D) 11.3 days
(E) 12.7 days
Rationale: Work done by 2 men and 3 women in 1 day = 1/10
Work done by 3 men and 2 women in 1 day = 1/8
Let 1 men does m work in 1 day and 1 women does w work in 1 day. The above equations can be written as
2 m + 3 w = 1/10 ---(1)
3 m + 2 w = 1/8 ---(2)
Solving equation (1) and (2) , we get m=14/200 and w=1/100
2 men and 1 woman together can finish the work in =14/200+1/100=2/25=12.5 days
B
Answer: (B) 12.5 days
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
(A) 16
(B) 13
(C) 15
(D) 18
(E) 12
Rationale: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15
Answer: C
Answer: (C) 15
Question: Andrew is selling fruit to be able to buy a new bike. The bike costs 400. He sells a large bag of fruit for $8. He so far has sold 32 bags, how many more need to be sold in order to buy the bike.
(A) 3
(B) 18
(C) 15
(D) 12
(E) 2
Rationale: 8*32=256
400-256=144
144Ã·8=18
18 more bags of fruit need to be sold in irder for the bike to be purchased.
Therefore answer B is correct.
Answer: (B) 18
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 7:00 am and Pipe B at 8:00 am, at what time will the pool be full?
(A) 16:00
(B) 18:00
(C) 19:00
(D) 20:00
(E) 17:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 7:00 a.m and Pipe B at 8:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 8:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 7:00 a.m, pool is full at 17:00 hrs
Answer : E
Answer: (E) 17:00
Question: A number increased by 10% gives 660. The number is?
(A) 200
(B) 300
(C) 500
(D) 600
(E) 400
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 10 % = 110 %
110 % -------> 660 (110 Ã— 6 = 660)
100 % -------> 600 (100 Ã— 6 = 600)
Option 'D'
Answer: (D) 600
Question: A driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?
(A) 14.2 km/h
(B) 17.1 km/h
(C) 19.3 km/h
(D) 21.7 km/h
(E) 23.5 km/h
Rationale: time 1 = d / 60
time 2 = d / 10
total time = d/60 + d/10 = 7d/60
average speed = total distance / total time = 2d / (7d/60) = 17.1 km/h
The answer is B.
Answer: (B) 17.1 km/h
Question: Walking at 3/4 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
(A) 36
(B) 48
(C) 60
(D) 62
(E) 66
Rationale: Let V be her normal speed and let T be her normal time.
D = (3/4)V * (T+12)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (3/4)V * (T+12)
T/4 = 9
T=36
The answer is A.
Answer: (A) 36
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 27, what is the value of a?
(A) 18
(B) 20
(C) 21
(D) 22
(E) 24
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 27:
9k/3 = 27
3k = 27
k=9
Then a=18.
The answer is A.
Answer: (A) 18
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 188 m
(B) 876 m
(C) 251 m
(D) 150 m
(E) 145 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: D
Answer: (D) 150 m
Question: According to a survey, at least 55% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
(A) 10%
(B) 20%
(C) 25%
(D) 0%
(E) 35%
Rationale: To minimize the percentage who like all three, let's maximize the percentage who like 2 out of 3.
80% like cherries and 20% don't like cherries.
Let's combine this with the people who like bananas.
20% don't like cherries but do like bananas.
55% like cherries and bananas.
25% like cherries but not bananas.
Now let's distribute the people who like apples.
20% like bananas and apples, but not cherries.
25% like cherries and apples, but not bananas.
10% like all three.
45% like cherries and bananas, but not apples.
The answer is A.
Answer: (A) 10%
Question: If 76 is divided into four parts proportional to 7,5,3,4, then the smallest part is
(A) 17
(B) 15
(C) 16
(D) 19
(E) 12
Rationale: Given ratio=7:5:3:4
Sum of ratio trems =19
Smallest part=(76x3/19)=12
ANSWER E 12
Answer: (E) 12
Question: The positive integers p and q leave remainders of 2 and 3, respectively, when divided by 6. p > q. What is the remainder when p – q is divided by 6?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: Let's test out some values of p and q that satisfy the given information.
p leaves are remainder of 2 when divided by 6
So, p COULD equal 8
q leaves are remainder of 3 when divided by 6
So, q COULD equal 3
What is the remainder when p – q is divided by 6?
So, p - q = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5
Answer: A
Answer: (A) 5
Question: A student can select one of 10 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
(A) 22
(B) 72
(C) 99
(D) 37
(E) 120
Rationale: 10C1×3C1×4C1 = 10x3x4=120 ways
Answer:E
Answer: (E) 120
Question: Simplify: 0.2*0.4+0.6*0.8
(A) 0.52
(B) 0.42
(C) 0.48
(D) 0.64
(E) 0.56
Rationale: Given exp. = 0.2*0.4+(0.6*0.8) = 0.08+0.48 = 0.56
Answer is E.
Answer: (E) 0.56
Question: Find the number of factors W of 180 that are in the form (4*k + 2), where k is a non-negative integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) W=6
Rationale: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 W(=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: (E) W=6