divelab/Sys2Bench huggingface dataset:
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
Options:
A)Rs. 28,000
B)Rs. 18,000
C)Rs. 14,000
D)Rs. 8,000
E)NONE OF THESE
Rationale: Explanation:
Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
ANSWER IS A
Answer: A
Question: 2,7,14,32,58,?
Options:
A)112
B)154
C)123
D)132
E)144
Rationale: 1^2+1=2
2^2+3=7
3^2+5=14
5^2+7=32
7^2+9=58
11^2+11=132
ANSWER:D
Answer: D
Question: If 30 honey bees make 30 grams of honey in 30 days, then 1 honey bee will make 1 gram of honey in how many days?
Options:
A)1
B)3.5
C)30
D)49
E)30
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 30 :: 30 : x
Honey 30 : 1
=> 1 x 30 x x = 30 x 1 x 30
=> x =30.
Answer : C
Answer: C
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability Q that the sum of the two integers will equal 9 ?
Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. Q=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: Q=1*1/5.
Answer: B.
Answer: B
Question: In a group of 65 people,40 like cricket,10 like both cricket and tennis. How many like tennis?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Make a Venn diagram, and enter your data.
Let the number of people who like only tennis be x
x + 10 + 30 = 65
x = 25
so number who like tennis = 10+25 = 35
Answer B
Answer: B
Question: 16 men and 12 children can complete work in 26 days 13 men can complete the same work in 48 days in how many days’ will12 men and 6 children complete half of the work?
Options:
A)12
B)15
C)13
D)14
E)None of these
Rationale: Explanation:
16 men and 12 children can do work in 26 days =>in one day
16 *26=416 men and 12*26=312 children can do same work
also, 13 men can do same work in 48 days =>13 *48=624 men
thus 624 men = 412 men + 312 children
=> 2mne = 3 children
24 men can do a work in 26 days
16 men can do same work in =26*24/16 = 39 days
Answer: Option D
Answer: D
Question: A man can row with a speed of 19 kmph in still water. If the stream flows at 8 kmph, then the speed in downstream is?
Options:
A)28
B)26
C)20
D)27
E)24
Rationale: M = 19
S = 8
DS = 19 + 8
=27
Answer: D
Answer: D
Question: A 60 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)A)73
B)B)20
C)C)83
D)D)17.1
E)E)52
Rationale: Explanation:
1: 2/5 = 5: 2
2/7 * 60 = 20
Answer: Option D
Answer: D
Question: The number of arrangements that can be made with the letters of the word MEAD so that the vowels occupy the even places?
Options:
A)6
B)5
C)4
D)10
E)21
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 2 places in 2! i.e., 2 ways.
Hence the total ways are 2 * 2 = 4.
Answer:C
Answer: C
Question: The interest on Rs.750 for 2yrs is the same as the True Discount on Rs.960 due 2yrs hence . If the rate of interest is same in both cases,it is:
Options:
A)12%
B)14%
C)15%
D)16%
E)26%
Rationale: Explanation:
S.I on Rs.750= T.D on Rs. 960
This means P.W of Rs. 960 due 2 years hence is Rs.750
Therefore , T.D= Rs. (960 - 750) = Rs. 210
Thus, S.I on Rs. 750 for 2 years is Rs. 210
∴Rate=[100×210/750×2]% = 14%
Answer: B
Answer: B
Question: What is the SI on Rs.8000 from August 6th to Dec 30th at 5% per annum rate of interest?
Options:
A)Rs 100
B)Rs 120
C)Rs 140
D)Rs 160
E)Rs 200
Rationale: Number of days from August 6th to December 30th = 146 days ( we don’t count the given day)
Simple Interest=
PTR
100
= 8000 x
146
365
x
5
100
= Rs 160
D
Answer: D
Question: Replace the ? by the correct Mathematics symbol to make the expression true
10 ? 10 ? 4 ? 7 = 18
Options:
A)10 ÷ 10 x 4 - 7 = 18
B)10 x 10 ÷ 4 - 7 = 18
C)10 + 10 ÷ 4 + 7 = 18
D)10 x 10 + 4 - 7 = 18
E)10 x 10 ÷ 4 + 7 = 18
Rationale: Answer : B
Answer: B
Question: Tanks M and B are each in the shape of a right circular cylinder. The interior of tank M has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank M is what percent of the capacity of tank B?
Options:
A)75%
B)80%
C)100%
D)120%
E)125%
Rationale: B.
For M, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
M/B = 160pi/200pi = 0.8
Answer: B
Question: Lloyd normally works 7.5 hours per day and earns $3.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
Options:
A)$33.75
B)$42.00
C)$51.75
D)$54.00
E)$70.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*3.5+ 3*3.5*1.5=42
Answer B
Answer: B
Question: To create paint with a certain shade of gray, one must combine 1.5 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
Options:
A)273.6
B)233.3
C)347.1
D)694.4
E)705.6
Rationale: Since the ratio of Black to White is 1.5 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 1.5:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. A is more than half so can not be the answer, B fits the criteria hence should be the correct answer. No calculation needed whatsoever.
Answer: B
Question: Find the simple interest on Rs.300 for 9 months at 6 paisa per month?
Options:
A)142
B)152
C)162
D)172
E)182
Rationale: I = (300*9*6)/100 = 162
ANSWER:C
Answer: C
Question: In one can of mixed nuts, 25% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
Options:
A)16 2/3%
B)30%
C)25%
D)33 1/3%
E)35%
Rationale: Can 1: size 1; 25% nuts
Can 2: size 0.5 and 40% nuts
(1x0.25+0.5x0.4)/1.5=30
B
Answer: B
Question: The median annual household income in a certain community of 21 households is $50,000. If the mean R income of a household increases by 10% per year over the next 2 years, what will the median income in the community be in 2 years?
Options:
A) $50,000
B) $60,000
C) $60,500
D) $65,000
E) Cannot be determined
Rationale: Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean R is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
Answer: E
Question: Find the length of the wire required to go 15 times round a square field containing 69696 m2.
Options:
A)15840
B)15848
C)15828
D)27892
E)22892
Rationale: a2 = 69696 => a = 264
4a = 1056
1056 * 15 = 15840
Answer:A
Answer: A
Question: In a panel of 10 light bulbs, the odds of any light bulb to burn out are 0.04 at any given 10 minutes. Should a light bulb burn out, the whole panel would instantly turn off. What are the odds that the panel would be turned off within the first 10 minutes after it was switched on?
Options:
A)1-0.04^10
B)1-0.96^10
C)(1-0.96)^10
D)0.06
E)1-10*0.06
Rationale: ans B.
Prob that light will not turned off = 0.96^10. Hence prob (turn off) = 1 - prob (not turn off).
Answer: B
Question: A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)4
B)5
C)6
D)9
E)8
Rationale: Sol.
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
= [66 * 5/18] m/sec = [55/3] m/sec.
∴ Time taken to pass the man = [110 * 3/55] sec = 6 sec.
Answer C
Answer: C
Question: Number of prime numbers between 40 and 70 is
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: total 7=41, 43, 47, 53, 59, 61, 67
ANSWER:D
Answer: D
Question: The average (arithmetic mean) monthly income of four workers is $5,000. After one worker’s income increases by 25 percent the new average income is $5,200. What was the original income of the worker whose monthly income increased?
Options:
A)$3,300
B)$3,600
C)$3,800
D)$4,200
E)$3,200
Rationale: Increase in total income was 200*4=$800, we know that this increase was 25% (1/4th) of the workers original income, thus his/her original income was 800*4=$3,200.
Answer:E
Answer: E
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
Options:
A)22
B)77
C)22
D)64
E)28
Rationale: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%.Answer:D
Answer: D
Question: The cost price of 20 books is the same as the selling price of ’X’ books. If the profit is 28%, then the value of X is ?
Options:
A)25
B)13.8
C)16
D)15
E)14
Rationale: let S.P. of X books = Rs 100 = C.P. of 20 books
Therefore, C.P. of one book = Rs 5.6
Profit = 28 %
Therefore, S.P of one book = 7.2
S.P of X articles = 7.2 X
7.2 X = 100 => X = 13.8
ANSWER:B
Answer: B
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 70 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?
Options:
A)(180-x)/2
B)(x+60)/4
C)21,000/(300+4x)
D)600/(115-x)
E)12,000/(x+200)
Rationale: E....
X% traveeled at 30 mph
100-X% traveeled at 70 mph
total timt taken = x/30 +(100-x)/70 = (300+4x)/210
Total distance = x+(100-x) = 100
Av speed = Tot Dis/Time Taken which is C
Answer: C
Question: A pipe can fill a cistern in 66 minutes. Find the time in which 1/11 part of the cistern will be filled?
Options:
A)5min
B)2min
C)6min
D)1min
E)10min
Rationale: Full cistern filled in = 66 minutes
1/11 part filled in = 66*1/11 = 6minutes
Answer is C
Answer: C
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
Options:
A)3337
B)2782
C)2788
D)4266
E)2321
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266
Answer:D
Answer: D
Question: A woman saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction
Options:
A)10%
B)12%
C)5%
D)15%
E)9%
Rationale: Price = 25+2.50 = 27.50
savings 2.5
percentage = 2.5/27.5*100
==> 9 %
ANSWER E
Answer: E
Question: Two pipes can fill a tank in 10 minutes and 25 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)30 minutes
B)17 minutes
C)7 minutes
D)10 minutes
E)12 minutes
Rationale: Part of the filled by all the three pipes in one minute
= 1/10 + 1/25 - 1/45 = (45 + 18 - 10)/450 = 53/450
So, the tank becomes full in 7 minutes.
Answer: C
Answer: C
Question: Working together, 7 identical pumps can empty a pool in 5 hours. How many hours will it take 4 pumps to empty the same pool?
Options:
A)4 2/3
B)9 1/4
C)9 1/3
D)8 3/4
E)10 1/2
Rationale: The answer is D
7 pumps take 5 hours. 1 Pump will take 5*7 hours . Hence 4 pumps will take (5*7)/4 = 8 75/100 = 8 3/4 hours
Answer: D
Question: In a certain conservative mutual fund, 70 percent of the money is invested in bonds, and of that portion, 40 percent is invested in highly rated corporate bonds. If at least $1.4 million in this fund is invested in highly rated corporate bonds, what is the smallest possible total value for the mutual fund?
Options:
A)$4 million
B)$5 million
C)$6 million
D)$7 million
E)$8 million
Rationale: Let x be the total money or value of the mutual fund.
Money in bonds=0.7x
Money in highly rated corporate bond= 0.4*0.7x=0.28x
0.28x > 1.4m
x > 1.4m/0.28 ; x > 140m/28 ; x>10 m/2 ;
so x > 5m
Smallest value is $ 5 million
ANSWER:B
Answer: B
Question: Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
Options:
A)300
B)800
C)1500
D)1200
E)1900
Rationale: (1/5)*2500 = 500
Remaining = 2500-500 = 2000
(1/4) of remaining = (1/4)*2000 = 500
Remaining now = 2000-500 = 1500
Answer: Option C
Answer: C
Question: If j < y < -1, which of the following is true?
Options:
A)j/y > jy
B)y/j > j+y
C)y/j > jy
D)y/j < j+y
E)y/j > j/y
Rationale: Consider :
j= -3
y= -2
then put for every option. U'll get ans B.
Answer: B
Question: 12, 34, 10, 11, 12, 5, 6 ,7, 13, 14, ?, ?
Logically, what two numbers should replace the question marks?
Options:
A)13 and 11
B)15 and 11
C)19 and 11
D)18 and 11
E)17 and 11
Rationale: B
15 and 11
1 + 2 + 3 + 4 = 10, then insert next two numbers 11, 12 and add digits
1 + 1 + 1 + 2 = 5.
Insert next two numbers 6, 7 and add digits 6 + 7 = 13. Insert next two numbers 14, 15 and add digits
1 + 4 + 1 + 5 = 11.
Answer: B
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 91 percent in some time period, which of the following could be the final mass of that element?
Options:
A)36 grams
B)28 grams
C)29 grams
D)31 grams
E)32 grams
Rationale: Let original mass be 100
The final mass of that element will be 9
So whatever option we have it will be divisible by 9
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 36 grams
36/9 = 4
B. 28 grams
28/9 = 3.111.....
C. 29 grams
29/9 = 3.222.......
D. 31 grams
31/9 = 3.444.....
E. 32 grams
32/9 = 3.555..
Answer (A)
Answer: A
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
Options:
A)Rs. 68
B)Rs. 70
C)Rs. 72
D)Rs. 88
E)Rs. 98
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: C
Question: It would take one machine 6 hours to complete a large production order and another machine 5 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
Options:
A)A 11/30
B)B 11/20
C)C 30/11
D)D 9/10
E)E 4/10
Rationale: The rate of the first machine is 1/6 job per hour;
The rate of the second machine is 1/5 job per hour;
Thus, the combined rate of the machines is 1/6+1/5=11/30 job per hour, which means that it takes 1/(11/30)=30/11 hours both machines to do the job.
Answer: C.
Answer: C
Question: The number of new words that can be formed by rearranging the letters of the word 'TOO' is?
Options:
A)1
B)5
C)11
D)4
E)2
Rationale: Number of words which can be formed
= 3! - 1 = 6- 1
= 5.
Answer:B
Answer: B
Question: How many multiples of 2 are there between 10 and 52, 10 and 52 inclusive?
Options:
A)27
B)25
C)24
D)21
E)22
Rationale: 2 multiples are ...10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,...,
the answer is =22
Answer is E
Answer: E
Question: Find the missing number in the given sequence : 2,4,6,8,10,?,14,?
Options:
A)11 & 15
B)12 & 16
C)13 & 15
D)12 & 18
E)11 & 17
Rationale: 2+2=4
4+2=6
6+2=8
8+2=10
10+2=12
12+2=14
14+2=16
ANSWER:B
Answer: B
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800
Options:
A)16
B)22
C)24
D)18
E)26
Rationale: Let the number of terms be N.
Then, according to the formula,
=> 1800 = N/2[2A+(N-1)D] , where A = First-Term, D = Common-Difference.
=> 3600 = N[12 + (N-1)6]
=> 3600 =N[6 + 6N]
=> 6N^2 + 6N - 3600 = 0.
=> 6N^2 + 150N - 144n - 3600 = 0
=> 6N(N + 25)-144(N+25)
=> N = -25, 24
Hence, the number of terms is 24.
ANSWER:B
Answer: B
Question: A train 800 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)87 Kmph
B)97 Kmph
C)72 Kmph
D)144 Kmph
E)120 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 800/20
S = 40 M/Sec
Speed= 40 *18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer: D
Answer: D
Question: A train 110 m long is running with a speed of 65 km/hr. In what time will it pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)4
D)8.2
E)5.5
Rationale: Speed of train relative to man =65+7= 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the men = 110 * 1/20 = 5.5 sec.
Answer: Option E
Answer: E
Question: The price of a Bicycle was increased by 50 percent. The new price was then increased by 30 percent. A single increase of what percent is equivalent to these two successive increases?
Options:
A)80%
B)75%
C)95%
D)85%
E)70%
Rationale: consider base price - $100
25% increase = 1.50*100 = $150
another 40% increase on new price = 1.3* 150 = $195
so final price of radio - $195
therefore a 95% increase
correct option - C
Answer: C
Question: How long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length?
Options:
A)9.8 sec
B)12.1 sec
C)12.42 sec
D)14.3 sec
E)24.3 sec
Rationale: 72 km/hr= 72*5/18 m/sec
= 20 m/sec
time= D/S = 110+132/20
= 242/20
= 12.1 sec
ANSWER:B
Answer: B
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 420 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
Options:
A)600
B)620
C)500
D)520
E)840
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 420) = 2 + 2(extra)
=> 2x - 840 = x => x = 840.
ANSWER:E
Answer: E
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
Options:
A)21 years
B)22 years
C)20 years
D)24 years
E)26 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+22.
=> 2(x+2) = (x+22+2)
=> 2x+4 = x+24
=> x = 20 years
Option C
Answer: C
Question: If U = V/W, -1 < W < 0 and 4 < V, which of the following is correct?
Options:
A)U > 4.
B)0 < U <4.
C)-4 < U < 0.
D)U < -4.
E)U < -20.
Rationale: V is +veW is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take V=4.1U=-0.9
U=4.1/-0.9
U<-4
Ans D
Answer: D
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
A)32 kmph
B)33 kmph
C)34 kmph
D)35 kmph
E)36 kmph
Rationale: A
32 kmph
S = (100 + 300)/45 = 400/45 * 18/5 = 32
Answer: A
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 4 children take to complete the work?
Options:
A)4
B)5
C)7
D)8
E)10
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 4 children)'s 1 day work
= (5/10 + 4/140) = 1/10
5 women and 4 children will complete the work in 10 days.
E
Answer: E
Question: Ayesha's father was30 years of age when she was born while her mother was 26 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)6 years
D)8 years
E)9 years
Rationale: Mother's age when Ayesha's brother was born = 26 years.
Father's age when Ayesha's brother was born = (30 + 4) years = 34 years.
Required difference = (34 - 26) years = 8 years. Answer: Option D
Answer: D
Question: Set T includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First, reach to the point of getting the equation T : x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: D
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √3 ¤ √3 =
Options:
A)0
B)5
C)12
D)15
E)20
Rationale: X = √3 and Y also =√3
Applying the function (√3+√3)^2 - (√3-√3)^2 = (2√3)^2 - 0 = 4 x 3 = 12.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√3 and y = √3 you get the answer 12.
Answer C
Answer: C
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $800. If each member of the club paid at least $53, then what is the greatest possible number of members in the club?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: 800/53=15 plus remainder.
The answer is A.
Answer: A
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
Options:
A)12 cm
B)10 cm
C)18 cm
D)24 cm
E)26 cm
Rationale: 30 * 20 * x = (8 * 5.5 * 1.5)/2
ANSWER:B
Answer: B
Question: What number is 60 more than two-fourth of itself?
Options:
A)180
B)225
C)288
D)324
E)336
Rationale: 2/4x+60= x
That means 60=2/4x
x= 60*3= 180
A is the answer
Answer: A
Question: The triplicate ratio of 1:6 is?
Options:
A)1:7
B)1:8
C)1:3
D)1:1
E)1:216
Rationale: 1^3: 6^3 = 1:216
Answer: E
Answer: E
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 30,000
B)Rs. 50,000
C)Rs. 60,000
D)Rs. 90,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 – x) respectively. Then,
1/3x=1/2(150000-x)
=> x/3 + x/2 = 75000
=> 5x/6 = 75000
=> x= 75000 x 6 /5= 90000
Savings in Public Provident Fund = Rs. (150000 – 90000) = Rs. 60000
Answer C
Answer: C
Question: In Orange County one fourth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
Options:
A)56.
B)42.
C)85.
D)145.
E)252.
Rationale: The number must be an integer and multiple of both 4 and 7.
Only option A fulfill this condition and hence is the answer.
Answer: A