mathewhe/aqua_rat huggingface dataset:
Question: On a scale that measures the intensity of a certain phenomenon, a reading of j+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
(A)  5
(B)  50
(C)  10^5
(D)  5^10
(E)  8^10 - 3^10
Rationale: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of j + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of j.”
Let’s practice this idea with some real numbers. Let’s say j is 2. This means that j + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.
4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.
5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.
Answer C.
Answer: (C)  10^5
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 11
(B) 30
(C) 99
(D) 48
(E) 61
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 800 * 3/50 = 48 sec.
Answer: D
Answer: (D) 48
Question: A clock loses 1% time during the first week and then gains 2% time during the next one week. If the clock was set right at 12 noon on a Sunday, what will be the time shown by the clock exactly 14 days from the time it was set right?
(A) 1: 36: 48
(B) 1: 40: 48
(C) 1: 41: 24
(D) 10: 19: 12
(E) None
Rationale: Solution:
The clock loses 1% time during the first week.
In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week.
If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.68 hours less.
Subsequently, the clock gains 2% during the next week. The second week has 168 hours and the clock gains 2% time = 2% of 168 hours = 3.36 hours more than the actual time.
As it lost 1.68 hours during the first week and then gained 3.36 hours during the next week, the net result will be a -1.68 + 3.36 = 1.68 hour net gain in time.
So the clock will show a time which is 1.68 hours more than 12 Noon two weeks from the time it was set right.
1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds.
i.e. 1 : 40 : 48 P.M.
Answer B
Answer: (B) 1: 40: 48
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 30 men in 3 days?
(A) 65mtr.
(B) 84mtr
(C) 70mtr.
(D) 78mtr.
(E) 17mtr.
Rationale: 20 men is 6 days can build 112 metres
30 men in 3 days can build = 112*(30/20)x(3/6)
= 84 meters
Answer: B.
Answer: (B) 84mtr
Question: Local kennel has cats and dogs in the ratio of 5:10. If there are 40 fewer cats than dogs, how many dogs are in the kennel?
(A) 80
(B) 70
(C) 60
(D) 50
(E) 45
Rationale: Lets work with the data given to us. We know that there ratio of cats to dogs is 5:10 or
cats 5
dogs 10
we can write number of cats as 5x and number of dogs as 10x and we know that 10x-5x= 40(therefore 5x = 40 => x=8)
Then # of dogs = 10x8= 80
Answer is A
Answer: (A) 80
Question: At a dinner party, 8 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 5040
Rationale: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position is fixed, the others can be arranged in 7! = 5040 ways.
Ans is E.
Answer: (E) 5040
Question: A train which has 400 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?
(A) 56 sec
(B) 40 sec
(C) 36 sec
(D) 29 sec.
(E) 19 sec.
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 400/((45-9) (5/18)
= 400/ 36*(5/18)
= 400/10
= 40 sec
ANSWER:B
Answer: (B) 40 sec
Question: A scientific research study examined a large number of young foxes, that is, foxes between 1 year and 2 years old. The study found that 80% of the young foxes caught a rabbit at least once, and 60% caught a songbird at least once If 10% of the young foxes never caught either a rabbit or a songbird, then what percentage of young foxes were successful in catching at least one rabbit and at least one songbird?
(A) 40%
(B) 50%
(C) 60%
(D) 80%
(E) 90%
Rationale: This is less about percents and more about probability, particularly the probability OR-rule. Let R = the event that a young fox catches at least one rabbit, and let S = the event that a young fox catches at least one songbird. Using algebraic probability notation, we know P(R) = 0.8 and P(S) = 0.6. We know P((not R) and (not S)) = 0.1, and the complement of [(not R) and (not S)] would be [R or S], so by the complement rule, P(R or S) = 1 – 0.1 = 0.9. The question is asking for P(R and S). The OR rule tells us
P(R or S) = P(R) + P(S) – P(R and S)
0.9 = 0.6 + 0.8 – P(R and S)
0.9 = 1.4 – P(R and S)
0.9 + P(R and S) = 1.4
P(R and S) = 0.5
Answer: (B) 50%
Question: The navy pilots are practicing flight formations. 200 pilots are practicing flying in rectangles. They want to make a rectangular formation with X planes in a row and Y planes in a column. If the
number of airplanes in a row is no less than 5 and no more than 40, how many different combinations of rectangular shapes are possible?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: firstly factors of 200 = 1,2,4,5,8,10,20,25,40,50,100,200
the question says each row will have airplanes not less than 5 and not more than 40,
therefore, we should be interested in the factors starting from 5 til 40 (inclusive)
5(in each row) * 40(number of columns) =200, similarly
8 * 25
10 * 20
20 * 10
25 * 8
40 * 5
total possibilities = 6
option A
Answer: (A) 6
Question: The food in a camp lasts for 40 men for 40 days. If ten more men join, how many days will the food last?
(A) 32days
(B) 34days
(C) 36days
(D) 38days
(E) 40days
Rationale: one man can consume the same food in 40*40 = 1600 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1600/50 = 32 days.
Answer: A
Answer: (A) 32days
Question: The triplicate ratio of 2:3 is?
(A) 1:64
(B) 1:62
(C) 1:34
(D) 8:27
(E) 5:64
Rationale: 2^3: 3^3 = 8:27
ANSWER:D
Answer: (D) 8:27
Question: The average of 100 numbers is 6, and the standard deviation is D, where D is positive. When added which of the following numbers, the new deviation will be less than D?
(A) -6 and 0
(B) 0 and 0
(C) 0 and 6
(D) 0 and 12
(E) 6 and 6
Rationale: The answer is E - 6 and 6
we can reduce the std.dev. by adding to integers equal to the mean - so answer is E.
Answer: (E) 6 and 6
Question: A person travelled from his house to office at 30km/hr and office to house at 20km/hr. Then find the average speed?
(A) 15km/hr
(B) 20km/hr
(C) 32km/hr
(D) 24km/hr
(E) 25km/hr
Rationale: Average speed = (2*30*20)/(30+20)
= 24km/hr
Answer is D
Answer: (D) 24km/hr
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
(A) 12
(B) 24
(C) 32
(D) 64
(E) 82
Rationale: Number of ways in which one can travel from P to R
=3×4=12=3×4=12
ANSWER A 12
Answer: (A) 12
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 70 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
(A) j/59
(B) 7j/500
(C) 140j
(D) j/100+40
(E) 140j/100
Rationale: lets take j=1000, as decided by you..
now 70% increase makes it 1700..
this is the price for 100 jackets, so selling price for each jacket=1700/100=$17..
so ans is correct as A..
Answer: (A) j/59
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.33 days
(C) 7.75 days
(D) 3.95 days
(E) 4.75 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer:A
Answer: (A) 3.75 days
Question: If 18 is 15 percent of 5 percent of a certain number, what is the number?
(A) 9
(B) 2400
(C) 40
(D) 81
(E) 400
Rationale: Let the certain number be x.
=> (15/100)*(5/100)*x = 18;
=> x=2400;
Ans is (B).
Answer: (B) 2400
Question: If 12 men or 20 women can do a piece of work in 27 days, then in how many days can 9 men and 12 women together do the work?
(A) 10 days
(B) 30 days
(C) 20 days
(D) 80 days
(E) 40 days
Rationale: C
20 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 27 days. So, 27 women can do it in (20 * 27) /27 = 20 days.
Answer: (C) 20 days
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 40
(B) 45
(C) 70
(D) 12
(E) 25
Rationale: Answer: Option C
a + b = 60, a = 2b
2b + b = 60 => b = 20 then a = 40.
5 years, their ages will be 45 and 25.
Sum of their ages = 45 + 25 = 70.
Answer: (C) 70
Question: If w = 20! + 17, then w is divisible by which of the following?
I. 15
II. 17
III. 19
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and II
Rationale: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.
So w!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.
Answer: (C)  II only
Question: A batsman makes a score of 83 runs in the 17th inning and thus increases his averages by 3.Find his average after 17th inning?
(A) 19
(B) 29
(C) 35
(D) 49
(E) 59
Rationale: let the average after 17th inning =x
Then average after 16th inning=(x-3)
Therefore 16(x-3)+83=17x
Therefore x=35
ANSWER:C
Answer: (C) 35
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 377
(B) 800
(C) 278
(D) 277
(E) 281
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Answer: (B) 800
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2 hours
(B) 9 hours
(C) 3 hours
(D) 7 hours
(E) 2 hours
Rationale: Part filled by A + B + C in 1 hour
= 1/5 + 1/10 + 1/30
= 1/3
All the three pipes together will fill the tank in 3 hours.
Answer:C
Answer: (C) 3 hours
Question: Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
(A) 6
(B) 8
(C) 10
(D) 14
(E) 16
Rationale: In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.
So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.
Answer: C.
Answer: (C) 10
Question: The price of a book is increased from $300 to $420. What is the % of increase in its price?
(A) 10%
(B) 20%
(C) 40%
(D) 50%
(E) 60%
Rationale: Explanation: Change in the price = Rs 420 â€“ Rs 300
= Rs 120
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 120 300
) *100 = 40%
C
Answer: (C) 40%
Question: The greatest number which on dividing 1442 and 1816 leaves remainders 12 and 6 respectively, is:
(A) 123
(B) 127
(C) 235
(D) 305
(E) 10
Rationale: Explanation:
Required number = H.C.F. of (1442 - 12) and (1816 - 6)
= H.C.F. of 1430 and 1810 = 10. Answer: E
Answer: (E) 10
Question: A can do a work in 20 days and B in 30 days. If they work on it together for 4 days, then the fraction of the work that is left is :
(A) 1/3
(B) 2/3
(C) 4/3
(D) 5/3
(E) 7/3
Rationale: Ans is:B
A's 1 day's work =1/20
B's 1 day's work =1/30
(A + B)'s 1 day's work =(1/20+1/30)=1/12
(A + B)'s 4 day's work =(1/12*4)=1/3
Therefore, Remaining work =(1-1/3)=2/3
Answer: (B) 2/3
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
(A) 147
(B) 258
(C) 451
(D) 361
(E) 420
Rationale: Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42;	7x= 84;	x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
Ans: E
Answer: (E) 420
Question: Along a yard 273 metres long, 14 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
(A) 18
(B) 19
(C) 10
(D) 21
(E) 12
Rationale: Explanation:
14 trees have 13 gaps between them,
Required distance (273/13) = 21
Option D
Answer: (D) 21
Question: A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train
(A) 70 km/hr
(B) 72 km/hr
(C) 79.2 km/hr
(D) 80 km/hr
(E) None
Rationale: Solution
Speed	= (132 / 6) m/sec
= (22 x 18 /5)km/hr
= 79.2 km/hr
Answer C
Answer: (C) 79.2 km/hr
Question: If an integer n is to be selected at random from 1 to 105, inclusive, what is probability n(n+1) will be divisible by 7?
(A) 1/7
(B) 3/14
(C) 1/2
(D) 2/7
(E) 3/4
Rationale: For n(n+1) to be a multiple of 7, either n or n+1 has to be a multiple of 7.
Thus n must be of the form 7k or 7k-1.
The probability is 2/7.
The answer is D.
Answer: (D) 2/7
Question: If both the product and sum of four integers are even, which of the following could be the number of even integers in the group?
I. 0
II. 2
III. 4
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: for four int to have their product and sum as even..
2 and 4 are ok..
but 0 even number will result in an odd integer as product..
ANSWER:D
Answer: (D) II and III only
Question: A person bought 135 glass bowls at a rate of Rs. 15 per bowl. He sold 115 of them at Rs. 18 and the remaining broke. What is the percentage gain for A?
(A) 40
(B) 30/11
(C) 20/9
(D) 27/11
(E) 29/8
Rationale: CP=135*15=2025 and SP=115*18=2070
Gain %= 100*(2070-2025)/2025= 20/9
ANSWER:C
Answer: (C) 20/9
Question: In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
(A) 8 1/3
(B) 8 1/6
(C) 8 1/9
(D) 8 1/1
(E) 8 1/5
Rationale: (4000*3*R)/100 = (5000*5*4)/100
R = 8 1/3
Answer: A
Answer: (A) 8 1/3
Question: On a Monday in a certain restaurant, 20 percent of the 180 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
(A) 15%
(B) 16%
(C) 18%
(D) 23%
(E) 30%
Rationale: 20% of 180= 36
10% of 120=12
Total =48
percent for 2 days combined =48/300 ≈ 50/300=1/6 =0.1666. so it should be less than 0.1666 so it is 16%
Another approach 48/300= 48/(3*100)= 16/100=0.16
Answer:B
Answer: (B) 16%
Question: emblem is coded as 216;
crude is coded as 125
bump will be ?
(A) 86
(B) 72
(C) 64
(D) 32
(E) 44
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
bump = 4^3 =64
ANSWER:C
Answer: (C) 64
Question: If 9210 - 9124 = 210-square, the value represented by the square is
(A) 296
(B) 210
(C) 186
(D) 124
(E) 24
Rationale: Evaluating the left side of the equation, we get 9210 -9124 = 86.
Therefore the right side of the equation, 210 - , must also equal 86.
Since 210 -124 = 86, then the value represented by the is 124.
correct answer D
Answer: (D) 124
Question: A baker charges W dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: We're told that by selling cakes at W dollars/cake, a baker will make $320.
Reducing the price by 20% and selling 2 MORE cakes will also make her $320.
We're asked for the original number of cakes that the baker intends to sell.
$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....
Let's TEST ANSWER D: 8 cakes
IF....
Original cakes = 8
8(W) = $320, so W = $40/cake
20% off = $8 off = 40-8 = $32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = $320
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D
Answer: (D) 8
Question: Bond (007) wants to move from a point A to point D, but here 2 watchtowers (B & C ) are present in the way of A to D. soldier on watchtowers has rifles with range of 1 kilometer. A,B,C,D are in straight line and distance between All points is 1 kilometer respectively. Find the minimum distance covered by 007 in journey between point A to D while his distance from watchtowers is always >=1 .
(A) 2.14
(B) 3.4
(C) 1.4
(D) 6.21
(E) 4.14
Rationale: bond has to travel on quarter circumference of circle centered B then wakl streight 1 km then again walk on circumference of circle centered C.
= 2*pi*1/4 + 2*pi*1/4 + 1
= 1.57 +1.57 + 1 =4.14
ANSWER:E
Answer: (E) 4.14
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 388
(B) 267
(C) 245
(D) 288
(E) 261
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: C
Answer: (C) 245
Question: What is the sum of the digits of integer k, if k = (10^50- 50)
(A) 337
(B) 437
(C) 457
(D) 537
(E) 412
Rationale: There are 51 digits in 10^50
When we subtract 50 from it, there will be 50 digits left.
10^50 can be written as 9999999....(50 times) + 1
So,
10^50 - 50 = 9999999....(50 times) + 1 - 50 = 9999999....(50 times) - 49
Consider the last 2 digits,
99-49 = 50
The last 2 digits will be 50.
And our number would be 99999......99950 with 2 less 9s after subtraction.
Number of 9s left are 48 and the last two digits are 50
The sum of the digits will be
(48*9) + 5 + 0 = 437
Answer:- B
Answer: (B) 437
Question: E, B, C are three consecutive positive integers (E>B>C). What is the value of the expression 2E +B +3C?
(A) 6A+7.
(B) 5A+1.
(C) 5A-1.
(D) 6A-5.
(E) 6E-7.
Rationale: => E+E+(E-1)+3(E-2)
Ans E. 6E-7.
Answer: (E) 6E-7.
Question: What is the greatest prime factor of 8!7! + 7!6! ?
(A) 7
(B) 11
(C) 13
(D) 17
(E) 19
Rationale: 8!7! + 7!6! = 7!6!(8*7+1) = 7!*6!*57 = 7!*6!*3*19
The answer is E.
Answer: (E) 19
Question: In Karthik's opinion, his weight is greater than 55 Kg but less than 62 Kg. His brother does not agree with Karthik and he thinks that Karthik's weight is greater than 50 Kg but less than 60 Kg. His father's view is that his weight cannot be greater than 58 Kg. If all of them are correct in their estimation, what is the average of different probable weights of Karthik?
(A) 54.5
(B) 56.5
(C) 59.2
(D) 61
(E) 62
Rationale: Explanation :
Solution: Assume Karthik's weight be x Kg.
According to Karthik, 55 < x < 62
According to Karthik;s brother, 50 < x < 60.
According to karthik's mother, x <58.
The values satisfying all the above conditions are 56 and 57.
.'. Required average = (56+57)/2 = 56.5.
Answer : B
Answer: (B) 56.5
Question: The banker's discount on Rs.1800 at 24% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
(A) 2 months
(B) 4 months
(C) 5 months
(D) 6 months
(E) 7 months
Rationale: Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 24%.
Time	=(100x72 / 24x1800)
= 1/6 year
= 2 months.
Answer A
Answer: (A) 2 months
Question: An investment compounds annually at an interest rate of 30% What is the smallest investment period by which time the investment will more than double in value?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239 > 2 (100)
;3 years;
ANSWER:A
Answer: (A) 3
Question: A hiker walking at a constant rate of 5 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 25 kilometers per hour. The cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: In 5 minutes, the cyclist travels a distance of (5/60)*25 = 25/12 km.
The time it takes the hiker to complete this distance is (25/12) / 5 = 5/12 hours = 25 minutes
The cyclist needs to wait 25 - 5 = 20 minutes
The answer is C.
Answer: (C) 20
Question: The diagonal of a square is 40 m. The area of the square is:
(A) 600
(B) 900
(C) 800
(D) 500
(E) 400
Rationale: Arear = 1/2 × ( diagonal )(power)2
= ( 1/2 × 40 × 40 )m(power)2
= 1600/2 = 800 m(power)2
Answer is C.
Answer: (C) 800
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
(A) 23
(B) 25
(C) 30
(D) 36
(E) 39
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: (C) 30
Question: A chemist mixes one liter of pure water with x liters of a 50% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3/7
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 50%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (50 - 15)/(15 - 0) = 7/3
1/x = 7/3
x = 3/7
Answer: E
Answer: (E) 3/7
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 67 days after his birthday?
(A) Thursday
(B) Friday
(C) Saturday
(D) Sunday
(E) Monday
Rationale: Day of week after 67 days after Arman's birthday = 7*9 + 4
Saturday as the period will have 9 weeks and 4 days .
The 4 days in the end will be Friday - Saturday - Sunday and Monday .
Answer E
Answer: (E) Monday
Question: The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
(A) 240
(B) 273
(C) 328
(D) 428
(E) 248
Rationale: A
240
Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
Answer: (A) 240