divelab/Sys2Bench huggingface dataset:
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)76 km
B)26 km
C)20 km
D)56 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2
=> x = 20 km.
Answer:E
Answer: E
Question: A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
Options:
A)3
B)6
C)9
D)10
E)12
Rationale: 221 + 43 = 264/17 = 9 (Remainder)
C
Answer: C
Question: A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)90
B)94
C)96
D)97
E)102
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
16x = 544
x = 34.
Hence, total number of notes = 3x = 102.
E
Answer: E
Question: A and B started a business. A invests rs.6000 and b invests rs.8000 after 6 months c joined them with rs.6000 but b left with the capital.after one year they get a profit of rs.2600.the share of A is?
Options:
A)900
B)1100
C)1200
D)1000
E)1300
Rationale: 6000x12 : 8000x:6 : 6000x6 = 6:4:3
so A work 2600x6/13 =1200
so ans is 1200
ANSWER:C
Answer: C
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
Options:
A)8
B)5
C)4
D)3
E)2
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer: A
Answer: A
Question: In Country Q, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
Options:
A) 50% decrease
B) 30% decrease
C) 15% decrease
D) 30% increase
E) 55% increase
Rationale: Country Q 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: B
Question: A certain college's enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options:
A)43%
B)45%
C)50%
D)35%
E)38%
Rationale: Suppose enrollment in 1991 was 100
Then enrollment in 1992 will be 130
And enrollment in 1993 will be 130*1.1=143
Increase in 1993 from 1991 = 143-100= 43
Answer : A
Answer: A
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors yellow, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: yellow, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
Options:
A)12
B)14
C)18
D)19
E)20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors yellow, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors yellow, purple, or orange (YPO).
#1: Pick one out of YPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of YPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of YPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: D
Question: Four years ago, the ratio of ages of P and Q was 5:3. Ten years from now, the ratio of their ages will be 6:5. What is P's age at present?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 3(P-4)/5 = (Q-4). Then Q = 3(P-4)/5 + 4
5(P+10)/6 = Q+10
5(P+10)/6 = 3(P-4)/5 + 14
25P+250 = 18P + 348
7P = 98
P = 14
The answer is D.
Answer: D
Question: Complete the sequence:
C E I O ?
Options:
A)M
B)W
C)S
D)D
E)Z
Rationale: C+2=E
E+4=I
I+6=O
O+8=W
B
Answer: B
Question: Rose's grade was 70th percentile of the 60 grades for her class. Of the 40 grades from another class, 16 were higher than Rose's, and the rest were lower. If no other grade was the same as Rose's grade, then Rose's grade was what percentile of the grades of the two classes of two classes combined?
Options:
A)66th
B)70th
C)74th
D)82nd
E)85th
Rationale: 66th/70th/74th/82nd/85th
Correct option: A
Answer: A
Question: The “a-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?
Options:
A) 3/8
B) 13/36
C) 17/36
D) 19/36
E) 23/36
Rationale: If you calculate 3^a for 1st roll, all 6 results will be 9, 81, 6561, 729, 9, 81. This result is the same for 2nd roll. 9, 81, 6561, 729, 9, 81.
About distance: If the first result is 9 and the second is also 9, the distance is 9-9=0 which is smaller than 9. If the first result is 9 and the second is 81, the distance is 81-9=72 which is also smaller than B which has the value of 81. If the first result is 81 and the second is 9, the distance will be greater than B. Distance 81-9=72>9.
On the first roll, the probability of getting result 9 is 2/6. In this case no other alternative values for second roll which would make the distance greater than B. So probability is 0. So next estimations are:
probability of getting 81 on the first roll (2/6) * probability of getting 9 on the second roll (2/6) = 1/9
probability of getting 729 on the first roll (1/6) * probability of getting 9, 81 on the second roll (4/6) = 1/9
probability of getting 6561 on the first roll (1/6) * probability of getting 9, 81, 729 on the first roll (5/6) = 5/36
All together: 1/9 + 1/9 + 5/36 = 13/36=B
Answer: B
Question: A present value of a machine is $800. Its value depletion rate is 10% per annum then find the machine value after 2 years?
Options:
A)$900
B)$810
C)$915
D)$715
E)$648
Rationale: P= $800
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=800*9/10 * 9/10
=$648
Answer is E
Answer: E
Question: If p and r are integers, and p^2 = 24r, then r must be divisible by which of the following?
Options:
A)2
B)3
C)5
D)7
E)14
Rationale: Ans: D
Solution: for p to be an int 24 r must be whole square of a number.
28r= 3*2*2*2*r
to make it whole square we need 3
so r can must be divisible by 3y where y is itself a whole square.
so B is the ans
Answer: B
Question: A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 20 balls per box. If 76 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?
Options:
A)2
B)1
C)4
D)6
E)8
Rationale: We have to work with multiples of 20 and 25.
First, we must know the limits of this multiples, so:
76/25= 3....so the max is 3
76/20=3...so the max is 3
76-75 =1
Answer : B
Answer: B
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
Options:
A)40
B)48
C)43
D)45
E)41
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3).
Then age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele.
Answer (D)
Answer: D
Question: Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
Options:
A)14 minutes
B)15 minutes
C)28 minutes
D)38 minutes
E)None of these
Rationale: Let the total distance to be covered is 48 kms.
Time taken to cover the distance without stoppage = 48/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 48/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.
ANSWER:E
Answer: E
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
Options:
A)1280π
B)75r
C)100r
D)24r
E)(64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 40 (8*5) while the smaller one has a diameter of 24 (8*3)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 40pi and 28pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.66 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.66 = 16.6 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.66 = 1000 revolutions per hour.
If r = 10, then the answer choice must be b.
C. 100r
Answer: C
Question: If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.150 then sum is
Options:
A)s.15000
B)s.15100
C)s.15800
D)s.16000
E)s.16200
Rationale: p(r/100)^2=C.I-S.I
P(10/100)^2=150
15000
ANSWER:A
Answer: A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)88
B)20
C)99
D)18
E)11
Rationale: Explanation:
C = 1/2 - 1/4 - 1/5 = 1/20 => 20 days
Answer:B
Answer: B
Question: Three people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)1/2
B)2/7
C)3/2
D)4/7
E)None of them
Rationale: Original share of 1 person = 1/3
New share of 1 person = 1/2
Increase = (1/2 - 1/3	= 1/6)
Therefore, Required fraction = (1/6)/(1/3)	= (1/6)x (3/1)	= 1/2
Answer is A.
Answer: A
Question: 1200 men have provisions for 18 days. If 450 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.0
C)12.5
D)12.2
E)13.1
Rationale: 1200*18 = 1650*x
x = 13.1
Answer:E
Answer: E
Question: If a+b+c=13, a2+b2+c2=69, then find ab+bc+ca
Options:
A)50
B)30
C)20
D)94
E)25
Rationale: (a+b+c)2= a2+b2+c2+2(ab+bc+ca)
2(ab+bc+ca)= (a+b+c)2- a2+b2+c2
=169-69
=100
ab+bc+ca=50
ANSWER A 50
Answer: A
Question: The letters E,A,W,D,S and R are rearranged to form the word 'Rewads'. Find its probability.
Options:
A)1/120
B)1/720
C)1/680
D)1/760
E)1/53
Rationale: Explanation :
There are total 6 letters. The probability that E gets the first position is 1/6.
The probability that A is in the second position is 1/5.
Likewise, probability for W,D,R and S are 1/4, 1/3,1/2 and 1/1.
Hence, the required probability is:-
=> (1/6) x (1/5) x (1/4) x (1/3) x (1/2) x 1.
=> 1/720.
Answer : B
Answer: B
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 21 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 11 books, how many shelves does the bookcase have?
Options:
A)8
B)6
C)4
D)3
E)2
Rationale: Let x be the number of shelves.
No of books in the beginning =11*x
After taking out 21 books No of remaining books = 11x -21
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+11
11x-21=8(x-1)+11
3x=24
x=8. Answer A
Answer: A
Question: A square carpet with an area 169 m2 must have 2 metres cut-off one of its edges in order to be a perfect fit for a rectangular room. What is the area of rectangular room?
Options:
A)180 m2
B)164 m2
C)152 m2
D)143 m2
E)None of these
Rationale: Side of square carpet = √Area=√169=13m
After cutting of one side,
Measure of one side = 13 – 2 = 11 m
and other side = 13 m (remain same)
∴ Area of rectangular room = 13 × 11 = 143 m2
Answer D
Answer: D
Question: One-third less than 20% of 180 is equal to:
Options:
A)24
B)30
C)35
D)40
E)45
Rationale: Lots of ways to tackle this.
20% of 180 =36
1/3 of 36= 12
So, 1/3,less than 36 is equal to 36- 12 = 24
Answer: A
Answer: A
Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on $4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Options:
A)$1750
B)$2250
C)$1250
D)$1500
E)$2000
Rationale: Compound Interest = (4000 x (1 + 10/100)^2 - 4000)
= 4000 x 11/10 x 11/10 - 4000 = 840
Therefore the sum is 420 x 100/(3 x 8) = 1750.
Answer A) $1750
Answer: A
Question: Average monthly income of a family of 4 earning members was Rs. 782. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
Options:
A)Rs. 1178
B)Rs. 820
C)Rs. 990
D)Rs. 1385
E)None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 782 x 4 - 650 x 3 Rs.
= 1178 Rs.
Correct Option: A
Answer: A
Question: At the start of the fall shopping season, a pair of boots cost $700. By the end of the season, the price was reduced to $420. If you waited to purchase the boots at the lower price, what percentage of the original price will you have paid?
Options:
A) 25%
B) 33%
C) 50%
D) 60%
E) 75%
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Here, we're told that the original price of the boots is $700 but that the purchase price is $420. We're asked what PERCENTAGE OF the original price is the purchase price.
Original Price = $700
Purchase Price = $420
The percentage of the original price of the boots:
$420/$700 = 3/5 = 60%
D
Answer: D
Question: Factor: 5x2 – 15x – 20.
Options:
A)5(x-4)(x+1)
B)-2(x-4)(x+5)
C)-5(x+4)(x-1)
D)5(x+4)(x+1)
E)6(x+4)(x+1)
Rationale: Solution:
5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
Answer: (A).
Answer: A
Question: with the digits 1,2,3,4,5,6 make all 6 digit nos which r not divisible by 5. The no of such 6 digit no's is ?
Options:
A)37,880
B)38,880
C)39,880
D)38,890
E)38,980
Rationale: 6c1*6c1*6c1*6c1*6c1*5c1 = 6*6*6*6*6*5
= 38,880
ANSWER:B
Answer: B
Question: Find the area of circle whose radius is 21m?
Options:
A)2884
B)1544
C)7674
D)1684
E)1386
Rationale: 22/7 * 21 * 21
= 1386
Answer: E
Answer: E
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
Options:
A)15.5
B)15
C)16
D)17
E)Cant be computed
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Option D
Answer: D
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is six times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
Options:
A)1:1
B)2:3
C)3:2
D)9:4
E)54:8
Rationale: Water:soap = 3:2
Soap:Salt=18:2
=> For 18 soap, salt = 2
=> For 2 Soap, salt = (2/18)*2 = 2/9
So, water:soap:salt = 3:2:2/9 = 54:36:4
After open container, water:soap:salt = 27:36:4
So, water:salt = 27:4 = 54:8
E
Answer: E
Question: In case R is the only individual sewing on committee B, which among the following shouldserve on committee A?
Options:
A)V and U
B)V and T
C)U and S
D)T and S
E)T and U
Rationale: T and S should serve on A
ANSWER:D
Answer: D
Question: An unbiased die is tossed. Find the probability of getting a multiple of 6
Options:
A)A)1/6
B)B)2/5
C)C)1/4
D)D)2/3
E)E)3/7
Rationale: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 3
E = {6}
P(E) = 1/6
Answer is A
Answer: A
Question: Ravish has to secure 40% marks to clear his board exam of class 10th.
He got 40 marks and failed by 40 marks.
What is the maximum marks ?
Options:
A)150
B)135
C)160
D)200
E)155
Rationale: D
200
To pass the exam ravish needs 40 + 40 = 80 marks.
=> (80/40) *100 = 200
Answer: D
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/7 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Options:
A)7/10
B)2/5
C)3/5
D)4/5
E)5/8
Rationale: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 3/4 * 4/7 X = 3/7 X
% loaded by day crew = X/(X + 3/7X) = 7/10
Answer A
Answer: A
Question: In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase?
Options:
A)16.66%
B)17%
C)15.8%
D)12%
E)None of these
Rationale: Explanation :
Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66%
Answer : A
Answer: A
Question: A tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 3.40%
B) 4.40%
C) 5.40%
D) 6.40%
E) 7.40%
Rationale: We start with 8,000 gallons of a solution that is 4% sodium chloride by volume. This means that there are 0.04 x 8,000 = 320 gallons of sodium chloride.
When 3,000 gallons of water evaporate we are left with 5,000 gallons of solution. From here we can determine what percent of the 5,000 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(320/5,000) x 100 = ?
0.064 x 100 = ?
= 6.4%
Answer is D.
Answer: D
Question: A and B start a business with Rs.3000 and Rs.9000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:5
B)1:5
C)1:3
D)3:1
E)3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
3000 : 9000 => 1:3,Answer: C
Answer: C
Question: Car A runs at the speed of 65km/hr & reaches its destination in 5hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 6
B)12 : 7
C)13 : 7
D)15 : 6
E)65 : 56
Rationale: Sol. Distance travelled by Car A = 65 Ã— 5 = 325 km
Distance travelled by Car B = 70 Ã— 4 = 280 km
Ratio = 325/280 = 65 : 56
E
Answer: E
Question: What is the ratio between perimeters of two squares one having 7 times the diagonal then the other?
Options:
A)3: 8
B)3: 6
C)3: 7
D)7: 1
E)3: 3
Rationale: d = 7d d = d
a√2 = 7d a√2 = d
a = 7d/√2 a = d/√2 => 7: 1
Answer:D
Answer: D
Question: Its a very poor village so sahara group organized a beneficiary cricket match for these people.
The event raised Rs300000.
Tickets were priced as follows:
Rs 748 for males
Rs 712 for ladies
Rs 45 for kids
How many males,ladies and kids were there ?
Options:
A)100 males , 209 ladies & 52 kids
B)120 males , 359 ladies & 72 kids
C)149 males , 259 ladies & 92 kids
D)150 males , 256 ladies & 92 kids
E)135 males , 259 ladies & 50 kids
Rationale: C
149 males , 259 ladies & 92 kids
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.1200 in 5 years?
Options:
A)12
B)3
C)14
D)5
E)6
Rationale: 450 = (750*5*R)/100
R = 12%.Answer: A
Answer: A
Question: If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
To illustrate consider adding:
*7
*7
...
77
77
----
=350
So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).
Answer: C.
Answer: C
Question: Best friends Sprite and Icey have are playing a game of marbles. They invite 4 of their friends to play with them. There are 36 marbles in the bag. If all 6 people are playing, how many marbles does each person get?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Answer= D
36 / 6 = 6
Answer= D
Answer: D
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)12
B)13
C)11
D)10
E)None of these
Rationale: Explanation:
Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
ANSWER IS D
Answer: D
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:
Options:
A)57.5 km/hr.
B)77.5 km/hr.
C)87.5 km/hr.
D)97.5 km/hr.
E)37.5 km/hr.
Rationale: C
87.5 km/hr.
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
Let the speed of two trains be 7x and 8x km/hr.
--> x = 100/8 = 12.5
--> Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
Answer: C
Question: (1^2+2^2+3^2+.....+9^2)=?
Options:
A)330
B)285
C)365
D)385
E)None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=9
=(1/6x9x10x19)
=285
Answer is B.
Answer: B
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 24km/hr, then find the area of square field.
Options:
A)125
B)225
C)256
D)425
E)None of these
Rationale: Explanation :
D = 24*3/2 = 36 km. So side of square is 16km, so area – 256km^2
Answer – C
Answer: C
Question: Jill has 7 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?
Options:
A)3
B)6
C)9
D)12
E)14
Rationale: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 7 1 3/4w = 7w=4The total number of jars = 3w =12Answer: D
Answer: D
Question: When a certain number X is divided by 95, the remainder is 31. What is the remainder when X is divided by 19?
Options:
A)10
B)11
C)12
D)15
E)17
Rationale: Let possible value of x is 126
least possible value of x/19 is 126/19 =>6 quotient with remainder 12
Thus answer is (C) 12
Answer: C
Question: The lowest number which should be added to 5915 so that the sum is exactly divisible by 3, 5, 8 and 7 is:
Options:
A)705
B)825
C)805
D)905
E)810
Rationale: L.C.M. of 3, 5, 8 and 7= 840.
On dividing 5915 by 840, the remainder is 35.
Number to be added = (840 - 35) = 805. Answer: Option 'C'
Answer: C
Question: (166)^2 - (167)^2 =
Options:
A)1
B)100
C)229
D)329
E)335
Rationale: Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 167*2 + 1
= 334+1 = 335 = Answer = E
Answer: E