mathewhe/aqua_rat huggingface dataset:
Question: Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year?
I.	Retirement age is 60 years.
II.	There are 50 employees in the department.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
I. Retirement age is 60 years.
II. There are 50 employees in the department.
Average age of 50 employees = 30 years.
Total age of 50 employees = (50 x 30) years = 1500 years.
Number of employees next year = 40.
Total age of 40 employees next year (1500 + 40 – 60 x 10) = 940.
Average age next year =940/40 years = 23 1/2 years
Thus, I and II together give the answer. answer is (E).
Answer: (E) Both I and II are necessary to answer
Question: In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 50 bricks in the wall, how many bricks does the bottom row contain ?
(A) 12
(B) 10
(C) 9
(D) 8
(E) 11
Rationale: The bottom row has x bricks
x+x-1+x-2+x-3+x-4 = 50
5x-10=50
5x=40
x=8
Answer:D
Answer: (D) 8
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
(A) 720
(B) 730
(C) 750
(D) 800
(E) 900
Rationale: Option 'A'
Answer: (A) 720
Question: Alice can fill Q cans of paint in 2 minutes. If there are R cans of paint in one gallon, how many gallons can Alice fill in 36 minutes?
(A) 36Q/R
(B) 18Q/R
(C) 18QR
(D) 18R/Q
(E) 36R/Q
Rationale: Alice can fill this number of cans in 36 minutes: (36/2)Q = 18Q.
One can is 1/R gallons.
Alice can fill 18Q*(1/R) = 18Q/R gallons of paint in 36 minutes.
The answer is B.
Answer: (B) 18Q/R
Question: The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 13%?
(A) 31.5%
(B) 35.9%
(C) 37.5%
(D) 39.5%
(E) 30.5%
Rationale: Let marked price = $100.
Then, C.P. = $64, S.P. = $87
Gain % = 23/64 * 100 = 35.9%. B
Answer: (B) 35.9%
Question: A is 6 times as fast as B and takes 100 days less to complete a work than B. Find the total number of days taken by A and B to complete the work.
(A) 120/7
(B) 120/9
(C) 120/76
(D) 120/6
(E) 120/1
Rationale: Explanation:-
According to question A is 6 times as fast as B
So, Ratio of time taken by A and B will be 1 : 6
Let time taken by A is = x
And time taken by B is = 6x
According to the question A take 100 days less
i.e. 6x – x = 100
x = 20
So, A takes 20 days and B takes 120 days to complete the work.
A's 1 day work = 1/20
B's 1 day work = 1/120
(A + B)'s 1 day work = 1/20 + 1/120 = 7/120
Total time taken = 120/7 days.
Answer: A
Answer: (A) 120/7
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 200 m
(B) 700 m
(C) 800 m
(D) 100 metre
(E) 1004m
Rationale: Explanation:
A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100 metre
Question: 5 x 1.6 - 2 x 1.4/1.3 = ?
(A) 3
(B) 0
(C) 5
(D) 4
(E) 2
Rationale: Given Expression
= (8 - 2.8)/1.3
= 5.2/1.3
= 52/1.3
= 4.
Answer is D.
Answer: (D) 4
Question: Find the odd man out
445, 221, 109, 46, 25, 11, 4
(A) 221
(B) 109
(C) 46
(D) 25
(E) 21
Rationale: 4*2+3 = 11
11*2+3 = 25
25*2+3 = 53
53*2+3 = 109
109*2+3 = 221
221*2+3 = 445
ANSWER:C
Answer: (C) 46
Question: Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 243^5?
(A) 5
(B) 8
(C) 10
(D) 15
(E) 25
Rationale: 243 = 3*3*3*3*3= 3^5
243^5 =(3^5)^5
=3^25
we have to find the greatest positive integer value for x
when x=25, it divides exactly once and that is the least positive integer value of the quotient
therefore, the correct option is E
Answer: (E) 25
Question: If p, q, and r are positive numbers such that (p/(p+q))(10) + (q/(p+q))(20)=r and if p<q which of the following could be the value of r?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: The answer is D. For any positive p and q, r is a number between 10 and 20. Since p < q, weight of 10 is inferior of weight of 20 -> r is > 15 -> 18 is the answer.
Answer: (D) 18
Question: A can do a piece of work 20 days. B can do work in 35 days. In how many days they will complete the work together?
(A) 15 days
(B) 16.32 days
(C) 12.72 days
(D) 17 days
(E) 18 days
Rationale: LCM = 140, Ratio= 20:35=4:7
No of days= 140/(4+7) = 90/5 = 12.72 days
ANSWER:C
Answer: (C) 12.72 days
Question: Each of the 48 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 15 students sign up for the poetry club, 23 students for the history club, and 21 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The total number in the three clubs is 15+23+21=59.
All 48 students signed up for at least one club.
3 of those students signed up for exactly one more club.
59 - 51 = 8 so 4 students must have signed up for exactly three clubs.
The answer is B.
Answer: (B) 4
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 32% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
(A) 35.67%
(B) 64.75%
(C) 68.00%
(D) 69.57%
(E) none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 32% of 1100 ) + ( 32% of 900)
= 352 + 288 = 640
Failed = 2000 - 640 = 1360
Failed % = [(1360/2000) x 100]%
= 68%.
ANSWER:C
Answer: (C) 68.00%
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid $ 2178?
(A) $ 2300
(B) $ 2650
(C) $ 2670
(D) $ 2200
(E) $ 2540
Rationale: D
$ 2200
Let the cost price of table for Sreenivas be $ x and given that, cost price of table for Mahesh = $ 2178.
=> (90%) of (110%) of x = $ 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = $ 2200
Answer: (D) $ 2200
Question: A shopkeeper sold an article at $100 with 30% profit. Then find its cost price?
(A) $120
(B) $100
(C) $91
(D) $77
(E) $69
Rationale: cost price = selling price *100/(100+profit)
C.P. = 100*100/130 = $77(approximately)
Answer is D
Answer: (D) $77
Question: The price of a VCR is marked at Rs. 12,000. If the successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
(A) Rs. 8400
(B) Rs. 8500
(C) Rs. 8721
(D) Rs. 8856
(E) None
Rationale: Solution
Actual price = 95% of 90% of 85% of
Rs. 12000.
= Rs. (95/100 x 90/100 x 85/100 x 12000)
= Rs. 8721.
Answer C
Answer: (C) Rs. 8721
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.9 sec
(C) 3.5 sec
(D) 7.5 sec
(E) 5 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 200/40
= 5 sec.
Answer: E
Answer: (E) 5 sec
Question: Sahil purchased a machine at Rs 12000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
(A) Rs. 22000
(B) Rs. 24000
(C) Rs. 26000
(D) Rs. 27000
(E) None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 12000 + 5000 + 1000 = 18000
150% of 18000 = 150/100 * 18000 = 27000
Option D
Answer: (D) Rs. 27000
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49
(B) 50
(C) 53.5
(D) 55
(E) 57
Rationale: Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2
Answer: A
Answer: (A) 49
Question: A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2400
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: Explanation:
Gain % = (164.36*100/2400) = 6.84 % = 7% approx
Option D
Answer: (D) 7%
Question: If two positive numbers are in the ratio 1/9 : 1/7, then by what percent is the second number more than the first?
(A) 67%.
(B) 70%.
(C) 60%.
(D) 28.6%.
(E) 80%.
Rationale: Given ratio = 1/9 : 1/7 = 7 : 9
Let first number be 7x and the second number be 9x.
The second number is more than first number by 2x.
Required percentage = 2x/7x * 100 = 28.6%.
Answer: D
Answer: (D) 28.6%.
Question: Which of the following fractions T, if written as a decimal, would have a 2 in the thousandths place ?
(A)  3/11
(B)  7/9
(C)  1/8
(D)  4/7
(E)  1/6
Rationale: (A) T=3/11 = 0.2727272727....
Answer: A
Answer: (A)  3/11
Question: What number has a 5:1 ratio to the number 10?
(A) 74
(B) 50
(C) 94
(D) 59
(E) 48
Rationale: Answer: Option B
Explanation:
5:1 = x: 10
x = 50
Answer: Option B
Answer: (B) 50
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 10 consecutive days in Rwanda?
(A) 4/7
(B) 3/7
(C) 105/512
(D) 4/28
(E) 28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
10C4 (1/2)^4 (1/2)^r
which is 105/512
Answer is C.
Answer: (C) 105/512
Question: A walks at 10 kmph and 10 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
(A) 100km
(B) 150km
(C) 50km
(D) 120km
(E) 200km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 10 hours.
x/10 - x/20 = 10
x = 200 km
Answer is E
Answer: (E) 200km
Question: 20% of a 6 liter solution and 60% of 4 liter solution are mixed. What percentage of the mixture of solution
(A) 36%
(B) 18%
(C) 35%
(D) 34%
(E) 30%
Rationale: 20% of 6 lit =6/5
60% of 4 lit =12/5
(6/5) + (12/5) =18/5
percentage of 10 lit = (18/5)*(1/10)*100 =36% ANSWER:A
Answer: (A) 36%
Question: Ravi purchased a car and a mobile phone for Rs. 150000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) loss of Rs. 200
(B) loss of Rs. 2000
(C) profit of Rs. 100
(D) profit of Rs. 200
(E) None of these
Rationale: Total C.P. = 150000+10000 = 160000
S.P. of car = 150000/100*98= 147000
S.P. of Mobile = 10000/100*110 = 11000
Total S.P. = 147000 + 11000 = 158000
Tota. S.P. - Total C.P. = 158000 - 160000 = -2000
Answer : B
Answer: (B) loss of Rs. 2000
Question: If a positive integer n is divisible by both 2 and 7, then n must also be divisible by which of the following?
I. 14
II. 9
III. 42
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Rationale: A multiple of 2 and 7 is also a multiple of 14, but not necessarily a multiple of 9 or 42.
The answer is B.
Answer: (B) I only
Question: A student chose a number, multiplied it by 4, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 60
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: Solution:
Let xx be the number he chose, then
4⋅x−138=102
4x=240
x=60
Answer A
Answer: (A) 60
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 289 m
(B) 676 m
(C) 240 m
(D) 239 m
(E) 186 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m
= 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540
==> x
= 240 m.
Answer:C
Answer: (C) 240 m
Question: If a is a positive integer then 6^(2a) + (144^a)/(2^(2a)) =
(A) 2 × 36^a
(B) 2 / 36^a
(C) 3 × 36^a
(D) 2 × 64^a
(E) 2 × 18^a
Rationale: 6^(2a) + 144^a/ 2^(2a) = 36^a + 144^a/4^a = 36^a + (144/4)^a = 36^a + 36^a = 2 × 36^a
Answer : A
Answer: (A) 2 × 36^a
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/16
(B) 30/10
(C) 30/14
(D) 30/13
(E) 30/11
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours. Answer:D
Answer: (D) 30/13
Question: The profit earned by selling on article for 900 is double the loss incurred when the same article is sold for 450. At what price should the article be sold to make 25% profit?
(A) 750
(B) 800
(C) 850
(D) 860
(E) 890
Rationale: Let ‘x’ be the CP of the article;
Then 900 – x = 2(x – 450); :. x= 600.
25% of 600 = 150
:. New SP = 600 + 150 = 750
Option 'A'
Answer: (A) 750
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 480. The number of hares in the zoo is?
(A) 40
(B) 99
(C) 77
(D) 66
(E) 221
Rationale: 200*2 = 400
480
-----
80
1----2
?----80 = 40
Answer:A
Answer: (A) 40
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
(E) Rs. 6976
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer:A
Answer: (A) Rs. 4991
Question: The probability of pulling a black ball out of a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
(A) 1/(XY).
(B) Y/X
(C) X/Y
(D) 1/(X+Y).
(E) 1/(X-Y).
Rationale: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.
Answer: (C) X/Y
Question: A statue is being carved by a sculptor. The original piece of marble weighed 200 kg. In the first week 20 percent is cut away. In the second week 25 percent of the remainder is cut away. In the third week the statue is completed when 35 percent of the remainder is cut away. What is the weight of the final statue?
(A) 97.5 kg
(B) 103 kg
(C) 108 kg
(D) 125 kg
(E) 117 kg
Rationale: A
97.5 kg
250 Ã— 0.8 Ã— 0.75 Ã— 0.65 = 97.5 kg.
Answer: (A) 97.5 kg
Question: A collection of books went on sale, and 2/3 of them were sold for $1.50 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
(A) $180
(B) $135
(C) $108
(D) $60
(E) $54
Rationale: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($1.50) or $108. The best answer is therefore C.
Answer: (C) $108
Question: If the perimeter of a rectangular garden is 500 m, its length when its breadth is 100 m is?
(A) 299 m
(B) 777 m
(C) 200 m
(D) 167 m
(E) 150 m
Rationale: 2(l + 100) = 500 => l
= 150 m
Answer:E
Answer: (E) 150 m
Question: At what rate percent on simple interest will Rs.1800 amount to Rs.2000 in 5 years?
(A) 4 %
(B) 3 6/7 %
(C) 2 6/7 %
(D) 3.47%
(E) 6 %
Rationale: Explanation:
250 = (1800x5xR)/100
R = 3.47%
Answer: Option D
Answer: (D) 3.47%
Question: we have 5 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg by using only four weight how many wight u can weight
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: select 4 weight out of 5, 5C4=5
ANSWER:E
Answer: (E) 5
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 25 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
(A) 36
(B) 2^4*3
(C) 24
(D) 38
(E) 47
Rationale: So 24 days
Answer C=24
Answer: (C) 24
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 14 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
(A) 12
(B) 14
(C) 10
(D) 11
(E) 13
Rationale: Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 8No. of days when B works = 6 → 8x + 6y = 1
When B starts:
No. of days when A works = 7No. of days when A works = 7 → 7x + 7y = 1
Solving the above two equations for xy
x = 1/14 y = 1/14
→ Total work done by AB in a day = 1/14 + 1/14 = 2/28= 1/14
→ No. of days to complete the work when both work together =14
Answer: B
Answer: (B) 14
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
(A) 70%
(B) 60%
(C) 30%
(D) 10%
(E) 20%
Rationale: Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer C
Answer: (C) 30%
Question: How much is 40% of 60 is greater than 4/5 of 25?
(A) 2
(B) 5
(C) 12
(D) 8
(E) 4
Rationale: (40/100) * 60 â€“ (4/5) * 25
24 - 20 = 4
Answer: E
Answer: (E) 4
Question: If 0.12 ÷ x2 = 12, than x = ?
(A) 0.001
(B) 0.01
(C) 0.1
(D) 1
(E) 0
Rationale: Explanation:
0.12 ÷ x2 = 12 => 0.12/x2 = 12
=> x2 = 0.12/12 = 0.01
=> x = 0.1
Answer: Option C
Answer: (C) 0.1
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 14 days
(B) 21 days
(C) 22 days
(D) 11 days
(E) 43 days
Rationale: D
11 days
x/24 + x/30 + x/40 = 1
x = 11 days
Answer: (D) 11 days
Question: From 2008 to 2009, the number of Easter eggs in a certain egg hunt rose 20%, then fell 17% from 2009 to 2010. From 2008 to 2009, the ratio of Easter eggs to Easter bunnies in the same hunt fell 20%, then rose 22% from 2009 to 2010. By what approximate percent did the number of bunnies change over the full period from 2008 to 2010?
(A) 5% increase
(B) 2% increase
(C) 1% decrease
(D) 3% decrease
(E) 6% decrease
Rationale: Let the number of Easter eggs be x1 in 2008 and x2 in 2010
Given that it rose 20% in 2009 and then fell 17% in 2010
=>x2 = (0.83)(1.2)x1 ---(1)
Let the number of Easter bunnies be y1 in 2008 and y2 in 2010
Given that the ratio of x to y fell 20% in 2009 and then rose 22% in 2010
=> x2/y2 = (0.8)(1.22)(x1/y1)
=> y1/y2 = (0.8)(1.22)(x1/x2) ----(2)
substituting (1) in (2),
y1/y2 = (0.8)(1.22)/(0.83)(1.2)
=> y2/y1 = (0.83)(1.2)/(0.8)(1.22) = 249/244
% change in y2 from y1 = (y2-y1)*100/y1
= (y2/y1 - 1)*100 = (249/244 - 1)*100
= (5/244)*100 = +2%
It's a 2% increase
Answer option "B"
Answer: (B) 2% increase
Question: If Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 12x/y
(B) 12y/x
(C) x/(12y)
(D) 13/(xy)
(E) xy/12
Rationale: This problem is testing us on the Rate x Time = Distance relationship. This relationship also tells us that Rate = Distance/Time and Time = Distance/Rate.
Ultimately, we are looking for how many seconds it will take Juan to run x yards. Thus, the equation we’ll use is: Time = Distance/Rate. We know the distance is x yards, and we need to find Juan’s rate.
We can find Juan’s rate as follows: Rate = Distance/Time = y yards/12 seconds
Using that rate, we need to determine how long it takes him to run x yards at the same rate. So we have:
Time = Distance/Rate
Time = x yards/(y yards/12 seconds)
Time = (x yards) x (12 seconds/y yards)
Time = 12x/y seconds
Answer A.
Answer: (A) 12x/y
Question: The area of a rectangular field is equal to 500 square meters. Its perimeter is equal to 90 meters. Find the width of this rectangle.
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: L * W = 500 : area , L is the length and W is the width.
2 L + 2 W = 90 : perimeter
L = 45 - w : solve for L
(45 - W) * W = 500 : substitute in the area equation
W = 20 and L = 25
correct answer D
Answer: (D) 20
Question: The sum of two numbers is 30 and their product is 1050. What will be the sum of their reciprocals?
(A) (1/35)
(B) (11/210)
(C) (35/4)
(D) (75/8)
(E) None
Rationale: Solution
x+y=30 xy=1050 1/x+1/y=x+y/xy 30/1050 = (1/35).
Answer A
Answer: (A) (1/35)
Question: Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 10^10+11^11 is divided by 5. What is the remainder?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a number is divisible by 5, if its last digit is divisible by 5
let's look into the sum of last digits of each term of the given expression
1^1=1
2^2=4
3^3=7
4^4=6
5^5=5
6^6=6
7^7=3
8^8=6
9^9=9
10^10=0
11^11=1
adding all these numbers we get 48 which gives a remainder of 3 when divided by 5. so answer must be 3.
bunuel, can you please confirm the answer of this question.
Yes, the OA is D. Clicked the wrong button when posting. Edited. Thank you.
D
Answer: (D) 3
Question: What is 35% of 4/13 of 780?
(A) 62
(B) 73
(C) 84
(D) 95
(E) 106
Rationale: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 780, or 1/9 of 780. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 780 is between 720 and 810, so (1/9)*780 will be between 80 and 90.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 84, so this is the answer to choose.
The answer is C.
Answer: (C) 84
Question: If a + b - c = 2d, and if a - b + c =-2e, then a =
(A) 2(d + e)
(B) d – e
(C) (d + e)/2
(D) d-2e
(E) e-d
Rationale: Add both equations:
a + b - c = 2d
a - b + c =-2e
a+b-c+a-b+c=2d-2e
2a=2d-2e
a=(d-e)
Ans:B
Answer: (B) d – e
Question: Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.
(A) 4000
(B) 5000
(C) 6000
(D) 7000
(E) None of these
Rationale: Explanation :
Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000. Answer : Option C
Answer: (C) 6000
Question: A typist uses a sheet measuring 20cm by 30 cm lenghtwise. If a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom, then what is the percentage of page used by the typist?
(A) 62 %
(B) 63 %
(C) 64 %
(D) 65 %
(E) 66 %
Rationale: Area of the sheet=(20*30)cm2= 600 cm2
Area used for typing=([20-4]*[30-6]) cm2 = 384 cm2
Therefore Required Percentage =(384/600)*100 = 64%
Answer C
Answer: (C) 64 %
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. metre
(A) Rs680
(B) Rs780
(C) Rs880
(D) Rs480
(E) Rs980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*80
= 68000p
in Rs =68000/100=Rs680
ANSWER:A
Answer: (A) Rs680
Question: A semicircle has a radius of 12. What is the approximate perimeter of the semicircle?
(A) 58
(B) 62
(C) 66
(D) 70
(E) 74
Rationale: The perimeter of a circle is 2*pi*r.
The perimeter of a semicircle is 2*pi*r/2 + 2r = pi*r + 2r
The perimeter is pi*12 + 2*12 which is about 62.
The answer is B.
Answer: (B) 62