mathewhe/aqua_rat huggingface dataset:
Question: If b is greater than 1 , which of the following must be negative?
(A) (2 - b)(b - 1)
(B) (b - 1)/3b
(C) (1 - b)^2
(D) (2 - b)/(1 - b)
(E) (1 - b^2)/b
Rationale: To be -ive, we should remember it should not be zero apart from being positive...
C will always be 0 or positive..
A and D will be zero at b=2..
B will always be positive..
left is E, where the numerator will always be negative and denominator, a positive..
ans E
Answer: (E) (1 - b^2)/b
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
(A) 1/7
(B) 3/7
(C) 2/7
(D) 6/7
(E) 5/7
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
ANSWER A
Answer: (A) 1/7
Question: Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 3 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y?
(A) 2y
(B) 4y
(C) 5y
(D) 6y
(E) 25/3y
Rationale: Anthony performed for 14 days meansw Cindy performed for(14-3)=11 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/11
Solving we get, x=25/3y
Now Anthony's Advance is x=25/3y .So answer should be E.
Answer: (E) 25/3y
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 8 kmph, then the speed of the boat in still water is :
(A) 2.5 km/hr
(B) 4.2 km/hr
(C) 5 km/hr
(D) 10.5 km/hr
(E) None of these
Rationale: Solution
Speed of stream = 1/2 (18-8) km/hr=5kmph . Answer C
Answer: (C) 5 km/hr
Question: A man bought 10 crates of mangoes for $160 total. If he lost 2 of the crates, at what price would he have to sell each of the remaining crates in order to earn a total profit of 25 percent of the total cost?
(A) $35
(B) $25
(C) $45
(D) $50
(E) $55
Rationale: As given, after lost, the remaining 8 crates total cost = $160
So, 1 crate cost = 160/8 = 20
To get 25% profit, 1 crate cost should be = 20+20*25/100 =$25
Answer : B
Answer: (B) $25
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 8 days more?
(A) 1122
(B) 1140
(C) 1199
(D) 1188
(E) 1166
Rationale: 760 ---- 22
760 ---- 20
x ----- 8
x*8 = 760*20
x = 1900
760
-------
1140
Answer: B
Answer: (B) 1140
Question: By weight, liquid X makes up 0.5 percent of solution P and 1.5 percent of solution Q. If 200 grams of solution P are mixed with 800 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.3%
(B) 1.2%
(C) 1.1%
(D) 1.0%
(E) 0.9%
Rationale: The number of grams of liquid X is 0.5(200)/100 + 1.5(800)/100 = 1 + 12 = 13 grams.
13 / 1000 = 1.3%
The answer is A.
Answer: (A) 1.3%
Question: In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides?
(A) 1, 2, 5
(B) 3, 4, 5
(C) 4, 5, 6
(D) 7, 8, 9
(E) 5, 2, 4
Rationale: XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option.
Answer: (B) 3, 4, 5
Question: How many Z ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
(A) 3
(B) 16
(C) 28
(D) 32
(E) 56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen Z= 56 - 24 = 32
Ans: D
Answer: (D) 32
Question: The average of 25 results is 50. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
(A) 741
(B) 752
(C) 878
(D) 785
(E) 458
Rationale: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*50
Or, x = 878.
Answer: Option C
Answer: (C) 878
Question: The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is ?
(A) 33.3
(B) 36.5
(C) 26.5
(D) 16.5
(E) 86.5
Rationale: Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B
Answer: (B) 36.5
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
(A) 33/91
(B) 33/18
(C) 33/29
(D) 33/18
(E) 33/12
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= 12C4/15C4
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:A
Answer: (A) 33/91
Question: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
(A) 89 days
(B) 90 days
(C) 85 days
(D) 99 days
(E) 79 days
Rationale: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.
Answer : D.
Answer: (D) 99 days
Question: At 15:00 there were 21 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?
(A) 7
(B) 14
(C) 25
(D) 27
(E) 30
Rationale: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -
8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)
20 + 3*14 -8 * 4 = 27
D
Answer: (D) 27
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) Rs.3750
(B) Rs.3000
(C) Rs.3200
(D) Rs.2160
(E) Rs.2000
Rationale: Explanation:
60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
ANSWER IS B
Answer: (B) Rs.3000
Question: There are 3 numbers x,y,z.the mean is m.median is 5.m is 10 more than the smallest number and 15 less than the biggest number.what is x+y+z?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: m=x+y+z/3
x+y+z=3m
median is middle number let y=5
let x is biggest number then x=m+15
z will be the smallest number then z=m-10
m+15+5+m-10=3m
m=10
then x+y+z=30
ANSWER:B
Answer: (B) 30
Question: whats the next no..
3,7,13,19....
(A) 27
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: prime no.s from 3 onwards
3,5,7,11,13,17,19,23,29
write alternate primes no.s starting from 3
3,7,13,19,29
ANSWER:C
Answer: (C) 29
Question: Nine children, Arya, Betsy, Chen, Daniel, Emily, and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?
(A) 240
(B) 480
(C) 540
(D) 720
(E) 840
Rationale: Since it is more time consuming and error prone to find ways Betsy and E not sitting together, It is better we find ways in which they will be together and then subtract from total ways..
total ways = 6!..
ways B and E will be sitting together..
take both B and E as one, then these two together with other 4 can sit in 5! ways ...
Also B and E can sit within themselves in 2! ways..
so the answer required = 6!-2*5!=840..
ans E
Answer: (E) 840
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) 299m
(B) 287m
(C) 279m
(D) 100m
(E) 277m
Rationale: 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) 100m
Question: If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let the roots of the equation 2a and 3a respectively.
2a + 3a = 5a = -(- 5/2) = 5/2 => a = 1/2
Product of the roots: 6a2 = b/2 => b = 12a2
a = 1/2, b = 3.
ANSWER:A
Answer: (A) 3
Question: The down stream speed of a boat is 50km/hr and its up stream speed is 10km/hr, then find the speed of boat in still water?
(A) 20km/hr
(B) 30km/hr
(C) 45km/hr
(D) 50km/hr
(E) 25km/hr
Rationale: speed of boat in still water = 1/2 (50+10) = 30 km/hr
Answer is B
Answer: (B) 30km/hr
Question: A report has 20 sheets each of 55 lines and each line consists of 65 characters. If this report is to be retyped with each sheet having 65 lines and each line of 75 characters what will be the reduction percent in the pages ?
(A) 22.5 %
(B) 35%
(C) 25%
(D) 15%
(E) 45%
Rationale: let 20 sheets contains 55*65*20 characters which is equals with y pages which contains 65*75*y characters .
Both the sheets have equal characters so, 20*55*65=y*65*75=>y=14.6 pages means 15 pages
so reduction in sheets =25%
ANSWER:C
Answer: (C) 25%
Question: Which of the following is equal to 1(3/5)%?
(A) 0.012/100
(B) 0.12/100
(C) 1.6/100
(D) 12/100
(E) 12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 1 and 3/5
How about adding a space:Which of the following is equal to (1 3/5)%
(1 3/5)% = 1.6% = 1.6/100
Answer:
C
Answer: (C) 1.6/100
Question: Which of these expressions has the greatest value?
(A) 1788542/1788545
(B) 1654321/1654326
(C) 1668421/1668424
(D) 1532156/1532159
(E) 1653782/1623787
Rationale: Using elimination method on options
1653782/1623787 = 1.01847225036...
ANSWER:E
Answer: (E) 1653782/1623787
Question: At the time of marriage, a man was 6 years elder to his wife. 12 years after their marriage, his age is 6/5 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
(A) 36 years
(B) 30 years
(C) 18 years
(D) 24 years
(E) 26 years
Rationale: let wifes age= x
husband age = x+6
now after 12 years of mrg x+12 wifes age
x+6+12 husbands age
6/5(x+12)=x+6+12
after solving x=18
ANSWER:C
Answer: (C) 18 years
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 22
(B) 56
(C) 88
(D) 66
(E) 21
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56'
Answer: B
Answer: (B) 56
Question: Of all the homes on Gotham Street, 1/3 are termite-ridden, and 4/7 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: The fraction of homes which are termite-infested but not collapsing is 3/7*1/3 = 1/7
The answer is E.
Answer: (E) 1/7
Question: By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 50?
(A) 5
(B) 4
(C) 11
(D) Not possible
(E) 8
Rationale: A number to be divisible by 50 must end with 00 or 50.
So, not possible.
Answer: D.
Answer: (D) Not possible
Question: Fred has 200 animals. If 6% are chickens, how many of the animals are not chickens?
(A) 12
(B) 24
(C) 198
(D) 188
(E) 156
Rationale: 6% of the 200 animals are chickens.
This means there are 200*(6/100) chickens.
Therefore 200 - 200*(6/100) animals are not chickens
200 - 200*(6/100) = X
200 - 1200/100 = X
200 - 12 = X
188
D)
Answer: (D) 188
Question: the sum of two numbers is 15 and their geometric mean is 20% lower than arithmetic mean . find the numbers .
(A) 11,4
(B) 12,3
(C) 9,6
(D) 3,2
(E) 2,1
Rationale: let a and b are two numbers
so a+b=15 ....(1)
now GM=AM*80/100
or, sqrt(ab)=[(a+b)/2]*80/100
squaring both sides...and after that putting the value of (a+b)...we get.....
ab=36 now go through from option then we get 12*3=36
ANSWER:B
Answer: (B) 12,3
Question: Last week John spent 10 percent of his wages on recreation. This week, his wages are 10 percent less than last weekʼs wages and he spent 40 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week
(A) 180%
(B) 360%
(C) 200%
(D) 220%
(E) 250%
Rationale: Say John's wages last week were $100, so he spent 0.10*100=$10 on recreation;
This week's wages is 0.90*100=$90, so he spends 0.4*90=$36 on recreation;
36/10=3.60, hence the amount he spends on recreation this week is 360% of the amount he spent on recreation last week: 10*3.6=36
Answer: B
Answer: (B) 360%
Question: If you are given $2, and the amount doubles every day, how much money will you have after 8 days?
(A) $256
(B) $512
(C) $1024
(D) $2048
(E) $4096
Rationale: 2^8=256
The answer is A.
Answer: (A) $256
Question: There are 40 balls which are red, blue or green. If 15 balls are green and the sum of red balls and green balls is less than 25, at most how many red balls are there?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: r+g+b=40
g=15
r + g < 25
=> r + 15 < 25
=> r < 10
=> at most 6 red balls
ANSWER:E
Answer: (E) 9
Question: Find the simple interest on Rs 8000 at 16% per annum for the period from 18th May 2014 to 8th April 2014
(A) Rs. 118.8
(B) Rs. 128.8
(C) Rs. 148.8
(D) Rs. 278.8
(E) Rs. 178.8
Rationale: Explanation:
One thing which is tricky in this question is to calculate the number of days.
Always remember that the day on which money is deposited is not counted while the day on which
money is withdrawn is counted.
So lets calculate the number of days now,
Time = (13+30+8) days = 51/365 years
P = 8000
R = 16%
S.I. = =8000Ã—16Ã— 51/(365*100)=178.8
Answer: E
Answer: (E) Rs. 178.8
Question: 19 5 17 = x
65 8 10 = y
What will be the value of x + y?
(A) 189
(B) 129
(C) 69
(D) 169
(E) 179
Rationale: according to options units digit is 9
7+1+1=9
10 's place +10's place+ unit place=1+1+7=9
according to this 5+1+6=12
so over all answer =129
ANSWER:B
Answer: (B) 129
Question: How long will it take a certain amount to increase by 30% at the rate of 15% simple interest?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the principal be Rs. x
Simple interest = x*30/100 = 3x/10
T = 100*SI/PR = 100*3x/10 / x*15 = 2%
Alternatively, this can be solved by considering principal amount to be Rs. 100. Then simple interest becomes Rs. 30. ANSWER : B
Then, T = 100*30/100*15 = 2%
Answer: (B) 30
Question: The value of x + x(xx) when x = 2 is:
(A) 10
(B) 18
(C) 16
(D) 64
(E) 36
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10CORRECT ANSWER : A
Answer: (A) 10
Question: __2A
x__B
____
CC
In the multiplication problem above, A, B, and C represent distinct digits. If the sum of A and B is equal to 4, what is the value of C?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: If A+B=4
assuming A and B are positive then A*B<10 (they could be either 1,2,3,)
therefore
A*B=C
2*B=C
A+B=4
Three simple equations - divide the 1st/2nd --> A=2 plug it the 3rd --> B=2 --> C=4 (ANSWER C)
Answer: (C) 4
Question: Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
(A) 11%
(B) 25%
(C) 44%
(D) 56%
(E) 125%
Rationale: ( Savings in Year 1 ) + ( Savings in Year 2 ) = 540
240 + ( Savings in Year 2 ) = 540
( Savings in Year 2 ) = 300
Increase in saving in Year 2 = 60 ( 300 - 240 )
% increase in savings = (60/240)100 =>25%
Hence answer will be (B) 25%
Answer: (B) 25%
Question: The ratio of the volumes of two cubes is 343 : 512. What is the ratio of their total surface areas?
(A) 1:22
(B) 8:12
(C) 36:41
(D) 81:19
(E) 1:11
Rationale: Ratio of the sides = ³√343 : ³√512
= 7 : 8
Ratio of surface areas = 72:82
= 36:41
Answer: C
Answer: (C) 36:41
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
(A) A)24
(B) B)25
(C) C)26
(D) D)27
(E) E)28
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER:A
Answer: (A) A)24
Question: The average marks of 10 students in a class is 100. But a student mark is wrongly noted as 60 instead of 10 then find the correct average marks?
(A) A)78
(B) B)82
(C) C)95
(D) D)91
(E) E)85
Rationale: correct avg marks = 100+(10-60)/10
avg = 100-5 = 95
Answer is C
Answer: (C) C)95
Question: A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 33
(B) 87
(C) 350
(D) 88
(E) 277
Rationale: D = 72 * 5/18 = 25 = 500 – 150 = 350
Answer:C
Answer: (C) 350
Question: A train 250 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 9 sec
(C) 12 sec
(D) 18 sec
(E) 15 sec
Rationale: Answer : E.
Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 50/3 m / sec = 250 *3/ 50 sec = 15sec
Answer: (E) 15 sec
Question: How many 6 digit number can be formed from the digits 1, 2, 3, 4, 5, 6 which are divisible by 4 and digits are not repeated?
(A) 192
(B) 122
(C) 140
(D) 242
(E) None of these
Rationale: Solution
For the number to be divisible by 4, the last two digits must be any of 12, 24, 16, 64, 32, 36, 56 and 52. The last two digit places can be filled in 8 ways. Remaining 3 places in 4P3 ways.
Hence no. of 5 digit nos. which are divisible by 4 are 24 × 8 = 192. Answer A
Answer: (A) 192
Question: x = 13.165
y = 7.496
z = 11.575
The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?
(A) 0.01
(B) 0.02
(C) 0.03
(D) 0.1
(E) 0.2
Rationale: Rounding off the values:
x = 13.17
y = 7.50
z = 11.58
A = 13.17 + 7.50 + 11.58 = 32.25
x + y + z = 13.165 + 7.496 + 11.575 = 32.206
B = 32.21
A - B = 0.03
Option C
Answer: (C) 0.03
Question: The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?
(A) 33
(B) 42
(C) 65
(D) 787
(E) 89
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Answer: (B) 42
Question: Three number are in the ratio 5:6:7. The sum of its largest and smallest numbers equals the sum of the third number and 48. Find the third number?
(A) 25
(B) 71
(C) 48
(D) 26
(E) 12
Rationale: Let the numbers be 5x, 6x and 7x.
Largest number = 7x
Smallest number = 5x
Third number = 6x
7x + 5x = 6x + 48
6x = 48
Third number is: 48.
Answer: C
Answer: (C) 48
Question: The average age of boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is
(A) 15 years
(B) 15.5 years
(C) 16 years
(D) 17 years
(E) Cannot be computed
Rationale: Clearly, to find the average,we ought to know the numbers of boys , girls or students in the class, neither of which has been given.
so the data provided is inadequate.
ANSWER:E
Answer: (E) Cannot be computed
Question: If 2x + 3y = 48; 2y + z = 19 and x + 2z = 29, what is the value of x + y + z ?
(A) 18
(B) 32
(C) 26
(D) 28
(E) None of these
Rationale: On solving equation we get
x = 15, y = 6, z = 7
Answer D
Answer: (D) 28
Question: The present population of a town is 2100. Population increase rate is 5% p.a. Find the population of town before 1 years?
(A) 1500
(B) 1600
(C) 2000
(D) 2100
(E) 2500
Rationale: P = 2100
R = 5%
Required population of town = P/(1 + R/100)^T
= 2100/(1 + 5/100)
= 2100/(21/20)
= 2000(approximately)
Answer is C
Answer: (C) 2000
Question: A circular ground whose diameter is 35 metres, has a 1.4 metre-broad garden around inside of it. What is the area of the garden in square metres?
(A) 301.5
(B) 484.12
(C) 401.84
(D) 301.0
(E) 301.84
Rationale: Req. area = Ï€[(35)2 â€“ (33.6)2]
= 22â„7 Ã— (68.6 Ã— 1.4)[since a2 - b2 = (a + b)(a - b)]
= (22 Ã— 68.6 Ã— 0.2 = 301.84 sq m.
Answer E
Answer: (E) 301.84
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length Q of a cube whose surface area is equal to 6z?
(A) Q=16
(B) Q=8√2
(C) Q=8
(D) Q=2√2
(E) (√2)/3
Rationale: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Answer: (D) Q=2√2
Question: Primary batteries, unlike secondary batteries, may be:
(A) 2
(B) 7
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
Primary batteries (disposable batteries), which are designed to be used once and discarded when they are exhausted.
Secondary batteries (rechargeable batteries), which are designed to be recharged and used multiple times.
Answer: Option B
Answer: (B) 7
Question: A contractor hires 100 men to finish a job in 50 days. After 8 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
(A) 21
(B) 18
(C) 16
(D) 12
(E) 8
Rationale: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.
Step 2 : After 8 Days = 8* 2= 16% of work is finished. remaining is 84% ( which means if same 100 men were about to complete the job they would have required 42 more days)
Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 42 days to compete for n people. at present 2n people are present to finish job. hence 21 more days.
A
Answer: (A) 21
Question: A man drives his car and starts with the speed of 25 kmph with its speed increasing every hour by 5 kmph. In how many hours would it take him to drive 100 kms?
(A) 4 1â„4 hours
(B) 3 1â„2 hours
(C) 3 hours 15 minutes
(D) Cannot be determined
(E) None of these
Rationale: Distance covered in first hour = 25 Ã— 1 = 25 km
Distance covered in next second hour = 30 Ã— 1 = 30 km
Distance covered in next third hour = 35 Ã— 1 = 35 km
Distance covered in first three hours
25 + 30 + 35 = 90 km
Remaining distance = 100 â€“ 90 = 10 km.
Now, this distance will be covered at the speed of 40 km/hr.
âˆ´ Time taken = 10â„40 = 1â„4 hour.
Total time= 3 + 1â„4 = 3 1â„4 hour
Answer C
Answer: (C) 3 hours 15 minutes
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 29
(B) 92
(C) 30
(D) 32
(E) 23
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: (C) 30
Question: The population of a bacteria culture doubles every 3 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
(A) 27
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: This one's easy.
1000 * 2^t = 500,000
2^t = 500
Now gauging, since 2^8 = 256, then 2^9 = 512
So t = 9
But be careful, 't' is in time intervals of 3 minutes
So answer is 9*3 = 27 minutes
Answer (A)
Answer: (A) 27
Question: (0.76)(power 3) - (0.1)(power 3)/ (0.76)(power 2) + 0.076 + (0.1)(power 2) is:
(A) 0.66
(B) 0.68
(C) 0.96
(D) 0.69
(E) 0.76
Rationale: Given expression
= (0.76) (power 3) - (0.1)(power 3) / (0.76)(power 2) + (0.76 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.76 - 0.1)
= 0.66
Answer is A.
Answer: (A) 0.66