mathewhe/aqua_rat huggingface dataset:
Question: Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
(A) (1/3)
(B) (1/8)
(C) (2/8)
(D) (1/16)
(E) (1/4)
Rationale: This is a simple division series; each number is one-half of the previous number.
In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8 and so on.
So the next number would be Option B.
Answer: (B) (1/8)
Question: Sachin is younger than Rahul by 4 years.If their ages are in the respective ratio of 7:9, how old is Sachin ?
(A) 24.5
(B) 29
(C) 31
(D) 26.5
(E) 30.5
Rationale: Let Rahul's age be x
then sachin's age = x-7
(x-7)/x = 7/9
9x-63 = 7x
x = 31.5
Sachin's age = x-7= 24.5 years
Answer is A
Answer: (A) 24.5
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 16 km/hr respectively. They will meet for the first time in?
(A) 50min
(B) 40min
(C) 35min
(D) 25min
(E) 36min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+16 = 36 km apart, they take 1 hour
To be 1000 m apart, they take 36 * 1000/1000 = 36 min.
Answer is E
Answer: (E) 36min
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $13,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
(A) 62,000
(B) 85,500
(C) 95,500
(D) 110,500
(E) 100,000
Rationale: Answer equals D in 48 years. I thought by 50th year it would reach 110,500. Options should have been separated more widely for clarity.
Answer: (D) 110,500
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 5 mangoes. Find the gain percent?
(A) 3.4%
(B) 2.5%
(C) 2.1%
(D) 8.5%
(E) 2.4%
Rationale: SP = CP + g
150 SP = 150 CP + 5 SP
145 SP = 150 CP
145 --- 5 CP
100 --- ? => 3.4%
Answer:A
Answer: (A) 3.4%
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4
Answer: D
Answer: (D) 4
Question: In how many ways 6 boys and 4 girls can be seated in a row so that they are alternative?
(A) 14420
(B) 12620
(C) 17280
(D) 21200
(E) 24560
Rationale: 6 boys can be seated in 6!
4 girls can be seated in 4!
Required number = 6!4! = 17280
Answer is C
Answer: (C) 17280
Question: Sheela deposits Rs. 5000 in bank savings account. If this is 20% of her monthly income. What is her monthly income in?
(A) 22000
(B) 20000
(C) 25000
(D) 22235
(E) None of these
Rationale: Explanation :
20% of income = Rs. 5000
100% of income = 5000 X 100/20 = Rs. 25000
Answer : C
Answer: (C) 25000
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 22 cm
(B) 24 cm
(C) 26 cm
(D) 28 cm
(E) 29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Answer: Option B
Answer: (B) 24 cm
Question: When a natural number N is successively divided by 11,12,13,14. the remainders are 15,16,17,18. What will be the sum of the remainders if the order of the division is reversed?
(A) 16
(B) 14
(C) 12
(D) 11
(E) 9
Rationale: 11 12 13 14
15 16 17 18
leave the top right- most number 8
start with bottom right-most number 5
18*13+17=251
251*12+16=3028
3028*11+15=33323
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 14
Hence, the correct option is B
Answer: (B) 14
Question: In a sports club with 40 members, 20 play badminton and 18 play tennis and 5 do not play either. How many members play both badminton and tennis?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 3
Rationale: 20+18=38
but where as total number is 40-5=35
therefore answer is 38-35=3
Hence Answer is E
Answer: (E) 3
Question: Peter purchased a machine for Rs.80,000 and spent Rs.5000 on repair and Rs.1000 on transport and sold it with 25% profit. At what price did he sell the machine?
(A) Rs.1,05,100
(B) Rs.1,06,250
(C) Rs.1,07,500
(D) Rs.1,17,500
(E) None
Rationale: Solution
C.P	= Rs.(80000+5000+1000)
= Rs.86000
Profit= 25%.
S.P	= 12.5% of Rs. 86000
=Rs.(125/100×86000)
=Rs.107500.
Answer C
Answer: (C) Rs.1,07,500
Question: If the side length of Square B is sqrt(3) times that of Square A, the area of Square B is how many times the area of Square A?
(A) 9
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Let x be the side length of Square A.
Then the area of Square A is x^2.
The area of Square B is (sqrt(3)x)^2=3x^2.
The answer is D.
Answer: (D) 3
Question: At a school, three-fourths of the male students and two-thirds of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?
(A) 2/3
(B) 3/5
(C) 4/5
(D) 7/10
(E) 13/20
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/4)(2/5)x = (3/10)x
The number of females who speak a foreign language is (2/3)(3/5)x = (2/5)x
The total number of students who speak a foreign language is (3/10)x + (2/5)x = (7/10)x
The answer is D.
Answer: (D) 7/10
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 15 m,17m
(B) 15 m,16m
(C) 15 m,10m
(D) 15 m,90m
(E) 15 m,30m
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: C
Answer: (C) 15 m,10m
Question: A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.
(A) Rs 2500
(B) Rs 32500
(C) Rs 22500
(D) Rs 32500
(E) Rs 12500
Rationale: Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100
x-[(5% of 10000 + 4% of (x-10000)]=31,100
x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100
x-500-((x-10000)/25)=31,100
x-(x/25)=31200  24x/25=31200x=[(31200*25)/24)=32,500.
Total sales=Rs.32,500
ANSWER D 32500
Answer: (D) Rs 32500
Question: Albert invested amount of 20000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
(A) Rs. 8510
(B) Rs. 22050
(C) Rs. 8730
(D) Rs. 8820
(E) None of these
Rationale: Explanation:
=>(20000×(1+5/100)2)
=>20000×21/20×21/20
=>22050
Option B
Answer: (B) Rs. 22050
Question: The value of x + x(x^x) when x = 4 is
(A) 1003
(B) 1024
(C) 1028
(D) 1026
(E) 1002
Rationale: Solution:
x + x(x^x)
Put the value of x = 2 in the above expression we get,
4 + 4(4^4)
= 4 + 4(4 Ã— 4 x 4 x 4)
= 4+ 4(256)
= 4 + 1024
= 1028
Answer: (C)
Answer: (C) 1028
Question: The value of a stock is X dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a quarter of its new value. What is the stock's value at the end of Monday?
(A) X.
(B) 3X/8.
(C) 2X/3.
(D) X/3.
(E) X/4.
Rationale: Stock value= X
AT sunday end= x+.5X= 1.5 X
On monday the value drop to 1/4rd of its value on sunday
1.5x/4= 3X/8
B is the answer
Answer: (B) 3X/8.
Question: A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere
interest rate is increased by 8%, it would amount to bow mucb ?
(A) Rs 990
(B) Rs 995
(C) Rs 997
(D) Rs 992
(E) Rs 999
Rationale: S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _
. R = ((100 x 120)/(800*3) ) % = 5%.
New rate = (5 + 3)% = 8%.
New S.l. = Rs. (800*8*3)/100 = Rs. 192.
:. New amount = Rs.(800+192) = Rs. 992
Answer is D.
Answer: (D) Rs 992
Question: Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
(A) 6
(B) 7
(C) 8
(D) 1
(E) 4
Rationale: 10*10
-------- = 1%
100
Answer: D
Answer: (D) 1
Question: Find k if 32 / k = 4.
(A) 6
(B) 7
(C) 8
(D) 4
(E) 3
Rationale: Since 32 /k = 4 and 32/ 8 = 4, then
k = 8 correct answer C
Answer: (C) 8
Question: Mary and Mike enter into a partnership by investing $900 and $100 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1600 more than Mike did, what was the profit made by their business in that year?
(A) $3500
(B) $3400
(C) $3300
(D) $3200
(E) $3000
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 9 : 1.
i.e., 90% of 2x would go to Mary and 10% of 2x would go to Mike.
Hence, Mary would get (90 - 10)% of 2x more than Mike
Or80% of 2x = $1600
i.e.,(60/100)*2x = 1600
or 2x = 2000.
Hence, the profit made by the company during the year $3x = $3000.
Answer : E
Answer: (E) $3000
Question: 75% of 480 = (?) x 15 ?
(A) 32
(B) 18
(C) 360
(D) None of these
(E) Cannot be determined
Rationale: Answer
Let 75% of 480 = A x 15.
⇒ (75 x 480)/100 = 15A
∴ A = (75 x 480)/ (100 x 15) = 24
Correct Option: D
Answer: (D) None of these
Question: A certain elevator has a safe weight limit of 1950 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Lets assume there are 2X people.
Half of them have average weight of 190 and other half has 200.
Maximum Weight is = 1950
So 190*X + 200*X = 1950
=> 390X = 1950
=> X is approximately equal to 5.
So total people is 2*5 = 10
Answer D.
Answer: (D) 10
Question: 69 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 20
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: According to the chain rule,
M1 x T1 = M2 x T2
Therefore, 69 x 12 x 5 = 30 x 6 x X
X = 23
Hence, the number of days = 23.
ANSWER:B
Answer: (B) 23
Question: If W + A < W - A < A - W, which of the following is correct?
(A) A < W < 0.
(B) W < A < 0.
(C) W < 0 < A.
(D) 0 < B < A.
(E) B > A > 0.
Rationale: Check first inequality
W + A < W - A
A<-A
A is -ve
Check another equality
W - A < A - W
-2A<-2W
A>W
Combining both 0>A>W
Option B fits only
Ans B
Answer: (B) W < A < 0.
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 43. Find the third number?
(A) A)37
(B) B)85
(C) C)48
(D) D)43
(E) E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 43
6x = 43 => third number is 43.
Answer: Option D
Answer: (D) D)43
Question: Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
(A) 22
(B) 11
(C) 44
(D) 33
(E) 55
Rationale: Let the numbers be 3x and 5x.
Then, 3x - 9/5x - 9 = 12/23
= 23(3x - 9)
= 12(5x - 9)
= 9x = 99
x = 11.
Therefore, The smaller number = (3 x 11) = 33.
Answer is D.
Answer: (D) 33
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.24000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 2:1
(C) 3:2
(D) 2:3
(E) 5:2
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:24000×9
=45×12:24×9
=15×12:8×9
=5:2
Answer is E.
Answer: (E) 5:2
Question: What day of the week was 5th January 2001
(A) Sunday
(B) Thursday
(C) Saturday
(D) Tuesday
(E) Friday
Rationale: Explanation:
5th Jan 2001 = (2000 years + 5th Jan 2001)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
5th Jan 2001 = 5 odd day
Total number of odd days = (0 + 5) = 5
5 odd days = Friday
Hence 5th January 2001 is Friday.
Answer: Option E
Answer: (E) Friday
Question: The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
(A) 1:1
(B) 1:9
(C) 1:3
(D) 1:4
(E) 1:3
Rationale: 1:4
Answer: D
Answer: (D) 1:4
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 2800
(B) 2500
(C) 2700
(D) 3000
(E) 3500
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 â€“ 5x/100 = 144
2x/100 = 56 Ã¨ x = 2800
ANSWER A
Answer: (A) 2800
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 40 years
(B) 50 years
(C) 60 years
(D) 70 years
(E) 80 years
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband’s present age = (90 – 50) years = 40 years.
Answer: A
Answer: (A) 40 years
Question: 5+8
(A) 8
(B) 13
(C) 28
(D) 6
(E) 2
Rationale: B
Answer: (B) 13
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 650?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 650 = 2*222 + (22*9) + 4*2
K weight of 600 = 2 +9+2 = 13
Answer D
Answer: (D) 13
Question: How many digits are in (8×10^18)(10×10^10)?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 30
Rationale: The question simplfies to (8×10^18)(10^11)
=> 8*10^29
=> Will contain 29 zeros +1 digit 8
=>30
Ans E
Answer: (E) 30
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent A of the interns report no feelings of tiredness during their shifts?
(A) 6
(B) 14
(C) 19
(D) 20
(E) 81
Rationale: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired A= 5 + 14 = 19.
Answer: C.
Answer: (C) 19
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12600 after a year?
(A) 3630
(B) 3637
(C) 3630
(D) 3631
(E) 3780
Rationale: 6300:4200:10500
3:2:5
3/10 * 12600 = 3780
Answer: E
Answer: (E) 3780
Question: 100 people standing in a circle in an order 1 to 100. No.1 has a sword. He kills next person (i.e.no. 2 )and gives sword to next to next (i.e no.3). All person does the same until only 1 survives. Which number survives at the last?
(A) 48
(B) 53
(C) 64
(D) 84
(E) 73
Rationale: my answer logic rules:
(i) if the last people survived of the next series remains same then the first person is killed
(ii)if the last person of the next sequence is less than the 1st series then the 1st person remains alive
(iii)all the sequence goes with an increment like 2,4,8,16,32,.....
these are the people survived
1,5,7,......99 (diff 2)
1,7,11,.....97 (diff 4),(here 97 1st will be killed
9,25,.......89 (diff 16)
9,41,73 (diff 32)
9,73 (diff 64)
73 is the last man to be alive
ANSWER:E
Answer: (E) 73
Question: There are 2 bars of copper-nickel alloy. One bar has 2 parts of copper to 5 parts of nickel. The other has 3 parts of copper to 5 parts of nickel. If both bars are melted together to get a 20 kg bar with the final copper to nickel ratio of 5:11. What was the weight of the first bar?
(A) 1 kg
(B) 4 kg
(C) 6 kg
(D) 14 kg
(E) 16 kg
Rationale: In the 20 KG bar,
Copper constitutes 5/16*20 = 25/4 of the mixture
Nickel constitutes 11/16*20 = 55/4 of the mixture
Now,
Let C/N ratio in Bar 1 of the solution be 2a : 5a
Let C/N ratio in Bar 2 of the solution be 3b : 5b
Therefore,
2a+3b = 25/4 and
5a+5b = 55/4
Solving for the above you get,
b= 3/4 and a=2
Now weight of the first bar = 2a+5a = 7*2 = 14
ANSWER:D
Answer: (D) 14 kg
Question: In certain code 'COLD' is written as '*$&#' and 'FOUND' is written as '@$^?#'. How is 'LOUD' written in that code?
(A) @%&#
(B) ?@^*
(C) #*&^
(D) &$^#
(E) #&^$
Rationale: & = L
$ = O
^ = U
# = D
Answer: Option D
Answer: (D) &$^#
Question: A hen leaps 6 leaps for every 8 leaps of a duck, but 4 leaps of the duck are equal to 3 leaps of the hen. What is the ratio of the speed of the hen to that of the duck?
(A) 1:1
(B) 3:8
(C) 4:3
(D) 8:9
(E) 1:3
Rationale: Given;
4 duck = 3 hen;
Or, duck/hen = 3/4;
Let hen's 1 leap = 4 meter and ducks 1 leap = 3 meter.
Then, ratio of speed of hen and duck = 4*6/3*8 = 1:1''Answer: 1:1;
Answer: (A) 1:1
Question: In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no 2 black balls are together
(A) 56
(B) 64
(C) 65
(D) 316
(E) 560
Rationale: Consider the possible arrangements:
WBWBWBWBWBWW or BWBWBWBWBWWW or WWBWBWBWBWBW or WWWBWBWBWBWB
Clearly, we are concerned about not placing 2 B's together, whites can be placed however we want.
So, it is like _W_W_W_W_W_W_W_ where black ball can be placed anywhere on the blank spaces, and this way, there never will be a case where 2 black balls fall together.
As there are 8 black spaces where 5 black balls can be placed, thus, the combination turns out as 8C5 (again, we are not concerned about the placement of white balls as we have already "fixed" their positions in the diagram above)
Also, we achieved at 8C5 as arranging 5 black balls on 8 different spots => 8!/5!3! (Total combination of available spaces = 8!; choosing 5 spaces out of them = 5!, arranging 3 leftover spaces = 3!) = 56
Hence answer is A
Answer: (A) 56
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 88
(C) 77
(D) 121
(E) 123
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄ = 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: (A) 360
Question: The length of the bridge, which a train 155 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 220 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (155 + x)/30 = 25/2
=> 2(155+ x)= 750 => x = 220 m.
Answer: C
Answer: (C) 220 m
Question: If v and d are both integers, v>d, and -3v>19, then the largest value of d would be?
(A) -5
(B) -6
(C) -7
(D) -8
(E) -10
Rationale: No, your thinking is incorrect. When we know that v>d and v<-6.33, the largest value of v can be -7 while if v=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<v and v = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: (D) -8
Question: GOOD is coded as 164 then BAD coded as 21.if ugly coded as 260 then ADD?
(A) 20
(B) 30
(C) 29
(D) 27
(E) 28
Rationale: GOOD=(7+15+15+4)*4=164
BAD= (2+1+4)*3=21
UGLY= (21+7+12+25)*4=260
coding follows
(sum of position of alphabets)*(no. of letters in the given word)
so,
ADD=(1+4+4)*3= 27
ANSWER:D
Answer: (D) 27
Question: What is the smallest positive integer x, such that 1944x is a perfect cube?
(A) 4
(B) 3
(C) 8
(D) 12
(E) 18
Rationale: Take out the factors of 1944 that will come 2^3*3^3 *3^2. for perfect cube you need every no. raise to the power 3. for 1944 to be a perfect cube, need 1 3 that means =3
B is the answer.
Answer: (B) 3
Question: (2^2+4^2+6^2+.....+14^2)=?
(A) 88
(B) 560
(C) 99
(D) 550
(E) 540
Rationale: =(1x2)^2+(2x2)^2,+(2x3)^3+......(2x7)^2
=2^2 x (1^2+2^2+3^2+.......+7^2)
formula is =1/6 n(n+1)(2n+1)
=(4x1/6x7x8x15)
=(4x140)=560
Answer is B
Answer: (B) 560
Question: A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:
(A) 90
(B) 100
(C) 110
(D) 140
(E) 150
Rationale: sax Letlheo g alnumberofworkers hex
x workers can do the wor - 100 days
(x — 10) workers can do the work in 110 days
4 100x 1u1x— 10)
1100 Q x 110
C
Answer: (C) 110
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%?
(A) 1
(B) 8
(C) 9
(D) 7
(E) 4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability K that each number is different ?
(A) A.18/25
(B) B.4/5
(C) C.81/100
(D) D.9/10
(E) E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability K= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: (A) A.18/25
Question: A train 50m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 15kmph
(B) 25kmph
(C) 35kmph
(D) 45kmph
(E) 55kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
50/[(x+5)*5/18] = 6
30(x+5) = 900
x = 25kmph
Answer is B
Answer: (B) 25kmph
Question: If in a race of 90m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
(A) 20m
(B) 16m
(C) 11m
(D) 10m
(E) 18m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (90 * 5) / 25 = 18m
Hence, A beats B by 18m.
ANSWER E
Answer: (E) 18m
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/11 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
(A) $110
(B) $120
(C) $183.3
(D) $220
(E) $260
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/11*(A+E) ==> 10A = 12E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2)
Substituting (1) in (2):
11A = 220+10A ==>A = 220 ;E =183.3
C
Answer: (C) $183.3
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) 540
(B) 325
(C) 600
(D) 455
(E) 200
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
ANSWER A
Answer: (A) 540