mathewhe/aqua_rat huggingface dataset:
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest Q?
(A)  60
(B)  61
(C)  62
(D)  63
(E)  64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=Q
answer is A.
Answer: (A)  60
Question: rahul played weel in this season.his current batting averagge is 53.if he score 78 runs in today match.his batting average will become 58.how many matches had he played in this season.
(A) 4
(B) 10
(C) 9
(D) 6
(E) 5
Rationale: 53x+78=58(x+1)
=>5x=20
=>x=4
ANSWER:A
Answer: (A) 4
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 249
(B) 178
(C) 245
(D) 277
(E) 121
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) 245
Question: A bowl has only 4 apples and 4 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
(A) 1/10
(B) 1/5
(C) 3/14
(D) 2/5
(E) 1/2
Rationale: 4/8 * 3/7
=3/14
C. 3/14
Answer: (C) 3/14
Question: John makes $60 a week from his job. He earns a raise and nowmakes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17%
(D) 17.2%
(E) 18%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?
(A) 7 km/hr
(B) 7.2 km/hr
(C) 7.5 km/hr
(D) 8 km/hr
(E) 8.9 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 30kmph and the other is going towards south 40kmph. What time will they take to be 50km apart?
(A) 1.32hr
(B) 0.714hrs
(C) 3.231hrs
(D) 0.515hrs
(E) 6.214hrs
Rationale: To be (30+40) km apart, they take 1 hour
To be 50 km apart, they take 1/70 *50 = 0.714 hrs
Answer is B
Answer: (B) 0.714hrs
Question: Half a number plus 5 is 11.What is the number?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let x be the number. Always replace "is" with an equal sign
(1/2)x + 5 = 11
(1/2)x + 5 - 5 = 11 - 5
(1/2)x = 6
2 × (1/2)x = 6 × 2
x = 12
correct answer is E)12
Answer: (E) 12
Question: If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 378 = 2 x 3 x 3 x 3 x 7
N must include at least 3, 2*3, and 3*3.
The answer is C.
Answer: (C) 9
Question: 5n + 2 > 12 and 7n - 5 < 23; n must be between which numbers?
(A) 1 and 8
(B) 2 and 4
(C) 0 and 9
(D) 2 and 7
(E) 2 and 9
Rationale: 5n > 10 --> n > 2
7n < 28 --> n < 4
2 < n < 4
Answer: B
Answer: (B) 2 and 4
Question: George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of Ford.
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Christopher age = x
George age, y = x + 8---------->(1)
Ford age, z = x - 2------------>(2)
Sum of their ages, x+y+z=60---->(3)
Substitute z and y values in equation (3)
Therefore, x+(x+8)+(x-2)=60
=> 3x+8-2=60
=> 3x=60-6
=> 3x=54 =>x=54/3
x=18(Christopher's age)
Substitute x value in equation 1 & 2
y=x+8
y=18+8
y=26(George's age)
z=x-2
z=18-2
z=16(Ford's age)
ANSWER:C
Answer: (C) 16
Question: A restaurant orders 150 kg of pumpkins from the farmer’s market. The farmer fills the order with 23 pumpkins. The average mass of the first 20 pumpkins is 6.5 kg. What must be the minimum average mass of the remaining 3 pumpkins to fill the order?
(A) 5.5 kg
(B) 5.67 kg
(C) 6.67 kg
(D) 7 kg
(E) 11.5 kg
Rationale: The order of 150 kg is distributed among 23 pumpkins.
20 of the pumpkins weigh a total of 20*6,5=130.
The remaining 3 pumpkins weigh a total of 150-130=20.
The average of the 3 remaining pumpkins(answer to the question) is 20/3=6,666... or 6,67.
Answer: C.
Answer: (C) 6.67 kg
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 11
(B) 25
(C) 77
(D) 88
(E) 11
Rationale: 800 --- 200
100 --- ? => 25%
Answer:B
Answer: (B) 25
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 24 gallons of ethanol, how many gallons of fuel A were added?
(A) 160
(B) 150
(C) 100
(D) 80
(E) 200
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 24 gallons then 0.12A+0.16(200-A)=24 --> A=200.
Answer: E.
Answer: (E) 200
Question: A is twice as good a workman as B and they took 8 days together to do the work B alone can do it in?
(A) 25 days
(B) 88 days
(C) 21 days
(D) 11 days
(E) 24 days
Rationale: WC = 2:1
2x + x = 1/8
x = 1/24 => 24 days
Answer: E
Answer: (E) 24 days
Question: Little John had $7.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left?
(A) $4.85
(B) $4.15
(C) $4.65
(D) $4.55
(E) $4.05
Rationale: John spent and gave to his two friends a total of
1.05 + 1.00 + 1.00 = $3.05
Money left
7.10 - 3.05 = $4.05
Answer :E
Answer: (E) $4.05
Question: If a and b are positive integers of B such that a/b=2.86, which of the following must be a divisor of a?
(A) 10
(B) B.13
(C) 18
(D) 26
(E) 50
Rationale: The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86
We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).
The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 143
B = 50
143/50 = 2.86
There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Final Answer:
B
Answer: (B) B.13
Question: 30^10 / 180^5=?
(A) 5^5
(B) 5^6
(C) 3^6
(D) 6^3
(E) 15^3
Rationale: 30^10 / 180^5=?
A. 5^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3
-> 30^10 / 180^5=(30^10)/(6^5)(30^5)=(30^5)/(6^5)=(6^5)(5^5)/(6^5)=5^5.
Thus, A is the answer.
Answer: (A) 5^5
Question: Each factor of 290 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 42?
(A) 1/16
(B) 5/42
(C) 16
(D) 3/16
(E) 1/4
Rationale: 290=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=1/6
Answer: C.
Answer: (C) 16
Question: A train 100 m long crosses a platform 125 m long in 40 sec; find the speed of the train?
(A) 36.21
(B) 77.11
(C) 54.12
(D) 33.0
(E) 20.25
Rationale: D = 100 + 125 = 225
T = 40
S = 225/40 * 18/5 = 20.25 kmph
Answer: E
Answer: (E) 20.25
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2356 sq m
(B) 1775 sq m
(C) 4312 sq m
(D) 1756 sq m
(E) 1765 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:C
Answer: (C) 4312 sq m
Question: A certain company reported that the revenue on sales increased 30 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
(A)  50 %
(B)  40 %
(C)  35 %
(D)  38 %
(E)  29 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 130 and and in 2005 180, so from 2003 to 2005 it increased by (180-130)/130=50/130=~38%.
Answer: D
Answer: (D)  38 %
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
(A) 7/13
(B) 11/12
(C) 12/10
(D) 23/50
(E) 19/77
Rationale: 12/10 it is
6/5=(1/2) + (1/5)
Answer - C
Answer: (C) 12/10
Question: There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?
(A) 22
(B) 87
(C) 26
(D) 19
(E) 36
Rationale: Explanation:
Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)
Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get
=> 2r = 72 => r = 36.
Answer: E
Answer: (E) 36
Question: If four coins are tossed, the probability of getting two heads and two tails is?
(A) 3/8
(B) 3/0
(C) 3/6
(D) 3/5
(E) 3/1
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer: A
Answer: (A) 3/8
Question: A race course is 400m long. A and B run a race and A wins by 5m. B and C run over the same course and B win by 4m. C and D run over it and D wins by 16m. If A and D run over it, then who would win and by how much?
(A) A, 8.4m
(B) D, 8.4m
(C) D, 7.2m
(D) A, 7.2m
(E) A, 9.2m
Rationale: when A covers 400m
B covers 395 m
c covers 391mtrs
and D covers 407.29 mtrs
ANSWER:C
Answer: (C) D, 7.2m
Question: Each child has 3 crayons and 12 apples. If there are 6 children, how many crayons are there in total?
(A) 22
(B) 65
(C) 18
(D) 36
(E) 10
Rationale: 3*6=18.Answer is C.
Answer: (C) 18
Question: Find the average of all the numbers between 6 and 39 which are divisible by 5?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 23
Rationale: Average = (10+15+20+25+30+35) 6= 135/6= 23
Answer is E
Answer: (E) 23
Question: A boy was asked to multiply a number by 22. He instead multiplied the number by 44 and got the answer 308 more than the correct answer. What was the number to be multiplied?
(A) 16
(B) 10
(C) 14
(D) 12
(E) 13
Rationale: Let required number
=x
=22x+308=44x
⇒22x=308
⇒x=308/22
=154/11
=14
Answer :C
Answer: (C) 14
Question: A bag contains 30 black balls and 20 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 2/5
(B) 5/7
(C) 1/2
(D) 1/4
(E) 1/3
Rationale: Total number of balls = 30+20 = 50
no. of white balls = 20
probability of drawing a white ball = 20/50 = 2/5
Answer is A
Answer: (A) 2/5
Question: Smith borrowed some money at the rate of 10% p.a. for the first 2years, at the rate of 12% p.a. for the next three years, and at the rate of 16% p.a. for the period beyond five years. If he pays a total interest of $ 600 at the end of 9years, how much money did he borrow?
(A) $1000
(B) $750
(C) $400
(D) $500
(E) $560
Rationale: Let the sum borrowed be x
(x*2*10/100)+(x*12*3/100)+(x*16*4/100) = 600
(20x/100)+(36x/100)+(64x/100) = 600
120x/100 = 600
x = 500
Answer is D
Answer: (D) $500
Question: A and B began business with Rs.2000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) 175
(B) 288
(C) 277
(D) 877
(E) 361
Rationale: (2*8 + 1*4):(4*8 + 5*4)
5:13
5/18 * 630 = 175
Answer: A
Answer: (A) 175
Question: In a camp, there is a meal for 120 men or 200 children. If 110 children have taken the meal, how many men will be catered to with remaining meal?
(A) 30
(B) 20
(C) 40
(D) 57
(E) 54
Rationale: There is a meal for 200 children.
110 children have taken the meal.
Remaining meal is to be catered to 90 children.
Now, 200 children 120 men.
90 children = (120/200)x 90 = 54 men.
E
Answer: (E) 54
Question: In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?
(A) 125.5 meters
(B) 126.5 meters
(C) 127.5 meters
(D) 128.5 meters
(E) 129.5 meters
Rationale: Explanation:
When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.
Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.
So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.
So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.
ANSWER IS C
Answer: (C) 127.5 meters
Question: A person crosses a 600 metre long street in 5 minutes. What is his speed in km per hour?
(A) 8.2
(B) 4.2
(C) 6.1
(D) 7.2
(E) 5.4
Rationale: Explanation:
Solution 1Distance =600 metre =0.6 km
Time =5=5 minutes =1/12 hour
Speed=distance/time=0.6/(1/12) =7.2 km/hr
ANSWER IS D
Answer: (D) 7.2
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 45
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
Option 'D'
Answer: (D) 40
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 801. What is the value of?
#
-##
____
812
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 100x
-(10x +x)
-----------
89 x= 801
x = 9
C
Answer: (C) 9
Question: A person can swim in still water at 16 km/h. If the speed of water 8 km/h, how many hours will the man take to swim back against the current for 12 km?
(A) 3
(B) 1.5
(C) 2.3
(D) 1.8
(E) 6
Rationale: M = 16
S = 8
US = 16 - 8 = 8
D = 12
T = 12/8 = 1.5
Answer: B
Answer: (B) 1.5
Question: A Man has 366 apples with him.If he were to distribute them equally between his none children what is the least number of mangoes that he has to add ?
(A) 2
(B) 3
(C) 1
(D) 14
(E) None
Rationale: B. (366+3=369). 369 is divisible by 9 369/9=41. So he will give 41 apples each to his nine children (41*9=369)
Answer: (B) 3
Question: There are 200 doctors and nurses at a hospital. If the ratio of doctors to nurses is 4 to 6, how many nurses are at the hospital?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: The number of nurses at the hospital is (6/10)*200=120.
The answer is B.
Answer: (B) 120
Question: Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.
(A) 27/34
(B) 29/34
(C) 50/34
(D) 55/34
(E) 60/34
Rationale: =>(9/17+8/16) + (8/17 + 9/16) + (9/17 + 8/16)
=>9/34+9/34+9/34 = 27/34
ANSWER A
Answer: (A) 27/34
Question: This is how Edward’s Lotteries work. First, 8 different numbers are selected. Tickets with exactly 6 of the 8 numbers randomly selected are printed such that no two tickets have the same set of numbers. Finally, the winning ticket is the one containing the 6 numbers drawn from the 8 randomly. There is exactly one winning ticket in the lottery system. How many tickets can the lottery system print?
(A)  8P6
(B)  8P3
(C)  9C9
(D)  8C6
(E)  69
Rationale: since we have to select random 6 numbers from 8 and they all are distinct. i think it should be 8C6 or D.
Answer: (D)  8C6
Question: Josh has to run an electrical wire from point a to point b along a circuit that is restricted to the grid shown to the left. How many possible paths could Josh use that have the minimum possible length?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 16
Rationale: ou can notice that in order the length to be minimum wire should only go UP and RIGHT: namely twice UP and 4 times RIGHT.
So combination of UURRRR: # of permutations of 6 letters out of which there are 2 identical U's and 4 identical R's is 6!/2!4!=15
Answer: D.
Answer: (D) 15
Question: Out of 16 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 12â„13
(B) 11â„13
(C) 9/11
(D) 1â„15
(E) None of these
Rationale: Total possible ways of selecting 4 students out of 16 students = 16C4 =1820
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 11C4=330
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 16C4 â€“ 11C4 = 1490
âˆ´ Probability = 1490â„1820 = 9â„11
Answer C
Answer: (C) 9/11
Question: In a kilometer race, A beats B by 100 meters or 10 seconds. What time does A take to complete the race?
(A) 290 sec
(B) 190 sec
(C) 199 sec
(D) 90 sec
(E) 193 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/100 = 100 sec.
Time taken by A = 100 - 10 = 90 sec.
Answer: D
Answer: (D) 90 sec
Question: Of the integers between 100 and 899, inclusive, how many do not have digit 2 and 5?
(A)  310
(B)  320
(C)  410
(D)  384
(E)  524
Rationale: Options for the first digit 8-2(2 and 5)=6;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 6*8*8=384.
Answer: D.
Answer: (D)  384
Question: A restaurant meal cost $45 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:
(A) $49 and $52
(B) $45 and $51
(C) $47 and 50
(D) $45 and $48
(E) $46 and $51
Rationale: let tip=t
meal cost=35.50
range of tip = from 10% of 45 to 15% of 45 = 4.5 to 6.75
hence range of amount paid= 45+T= 49.5 to 51.75 i.e. A
Answer: (A) $49 and $52
Question: The number N is 5,H64, where H represents the hundred's digit. If N is divisible by 4, what is the value of H?
(A) 0
(B) 1
(C) 2
(D) 5
(E) All the above value
Rationale: If the number is divisible by 4, the last two digits must be divisible by 4. All the values yields such a number.
Answer: E
Answer: (E) All the above value
Question: 1,3,5,7,9,..50 find term of sequnce
(A) 1234
(B) 1456
(C) 1456
(D) 1678
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: (E) 2500
Question: In 1 hour, a boat goes 9 km along the stream and 3 km against the stream. The speed of the boat in still water (in km/hr) is :
(A) 3 km/hr.
(B) 2 km/hr.
(C) 6 km/hr.
(D) 8 km/hr.
(E) 5 km/hr.
Rationale: Speed in still water = 1/2(9 + 3) km/hr
= 6 km/hr. ANSWER :C
Answer: (C) 6 km/hr.
Question: A and B enterd into a partnership investing Rs.16,000 and Rs.12,000 respectively.After 3 months,A withdrew Rs.5000 while B invested Rs.5000 more.After 3 more months.C joins the business with a capital of Rs.21,000.The share of B exceeds that of C,out of a total profit of Rs.26,400 after one year by
(A) Rs.2400
(B) Rs.3000
(C) Rs.3600
(D) Rs.4800
(E) None of these
Rationale: Solution
A : B : C = (16000x3+11000x9) : (12000x3+17000x9): (21000x6)
= 147 : 180 : 126 = 7 : 9 : 6.
∴ Difference of B and C’s shares = Rs. (26400x9/22-26400x6/22) = Rs. 3600. Answer C
Answer: (C) Rs.3600
Question: A & B can separately do a piece of work in 20 & 15 days. They worked together for 6 days, after which B was replaced by C. The work was finished in next 5 days. The no.of days in which C alone could do the work is
(A) 10 days
(B) 20 days
(C) 30 days
(D) 40 days
(E) 50 days
Rationale: B worked for 6 days => In 6 days B completed = 6 x 1 15
= 2 5
th work
A worked for first 6 days and later 4 days => In 10 days A completed = 10 x 1 20
= 1 2
of the work
Total work done by A and B = 2 5
+ 1 2
= 4+5 10
= 9 10
Balance work = 1- 9 10
= 1 10
th of total work
Balance work was completed by C in 5 days
C can do 1/10 of the work in 5 days. Therefore C alone can do the work in 50 days.
E
Answer: (E) 50 days
Question: A crate of apples contains 1 bruised apple for every 35 apples in the crate. Two out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 10 apples not fit to sell in the crate, how many apples are there in the crate?
(A) 270
(B) 360
(C) 700
(D) 600
(E) 840
Rationale: as given 2 out of every 4 bruised apple is not fit to sell
or, 50% of the bruised apples are not fit to sell.
as per the question 10 are not fit to sell
or,
0.50x=10
x=1000/50=20
thus total number of bruised apples =20
total number of apples =35*20=700
Answer: C
Answer: (C) 700
Question: If x and y are positive integers, and x^3*y^4 = 16, which of the following is the value of xy?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 16 = 1^3*2^4
xy = 1*2 = 2
The answer is A.
Answer: (A) 2
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 245
(B) 777
(C) 282
(D) 266
(E) 288
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
Answer: C
Answer: (C) 282
Question: The average age 11 members of a committee are the same as it was 5 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 20 years
(B) 21 years
(C) 18 years
(D) 55 years
(E) 30 years
Rationale: 11 * 5 = 55 years
Answer:D
Answer: (D) 55 years
Question: Average weight of 10 people increased by 1 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: Explanation:
Total weight increased is 1 * 10 = 10.
So weight of new person is 45+10 = 55
Answer: Option B
Answer: (B) 55
Question: A sum was put at simple interest at a certain rate for 5 years Had it been put at 6% higher rate, it would have fetched 90 more. Find the sum.
(A) 90
(B) 100
(C) 200
(D) 300
(E) 400
Rationale: Difference in S.I. = P×T/100(R1−R2)
⇒ 90 = P×5x6/100(∵ R1 - R2 = 2)
⇒ P = 90×100/5x6=300
Answer D
Answer: (D) 300
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 288 cm2
(B) 277 cm2
(C) 285 cm2
(D) 276 cm2
(E) 287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: (C) 285 cm2
Question: What will come in place of (a) in the following expression?
a - 896.21 + 498.05 = 215.50 – 425.01
(A) 188.65
(B) 88.6
(C) 188.67
(D) 83.65
(E) 88.61
Rationale: Explanation:
a - 896.21 + 498.05 = 215.50 - 425.01
a = 188.65
ANSWER: A
Answer: (A) 188.65
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.4 per sq m?
(A) 2288
(B) 2779
(C) 2779
(D) 5200
(E) 2781
Rationale: Area = (l + b â€“ d) d
(80 + 60 â€“ 10)10 => 1300 m2
1300 * 4 = Rs.5200
Answer:D
Answer: (D) 5200