mathewhe/aqua_rat huggingface dataset:
Question: Out of four numbers ,the average of first three is 20 and that of the last three is 15. If the last number is 18,the first number is :
(A) 22
(B) 33
(C) 77
(D) 99
(E) 27
Rationale: Explanation:
Let the numbers be a,b,c,d
Given, a + b + c = 60, b + c + d = 45
Now, d = 18
thus, b + c + 18 = 45 ⇒ b + c = 27
Putting the value of b + c in a + b + c = 60
a + 27 = 60 ⇒ a = 33
Answer: B
Answer: (B) 33
Question: If (a) '1 2 3' stands for 'These are girls', (b) '135' stands for 'girls are clever' and (c) '156' stands for 'clever girls sing', which numerical stands for 'clever'?
(A) 1
(B) 4
(C) 2
(D) 3
(E) 5
Rationale: Explanation:
(a) '1 2 3' ===>'these are girls'
(b)'1 3 5' ===>'girls are clever'
(c)'1 5 6' ===>' clever girls sing'
From statements (a) and (b) above we can notice that the set of numbers “1” and ”3” would stand for the set of words “girls ” and “are” (through not respectively). Thus the code number for clever would be “5” ( and the code number for “these” would be “2”). The statement (c) becomes redundent. (superfluous)
ANSWER: E
Answer: (E) 5
Question: The length of minute hand of a clock is 5.4 cm. What is the area covered by this in 20 minutes
(A) 15.27
(B) 16.27
(C) 17.27
(D) 30.54
(E) 30.27
Rationale: area of circle is pi*r^2
but in 20 minutes area covered is (20/60)*360=120 degree
so formula is pi*r^2*(angle/360)=3.14*(5.4^2)*(120/360)=30.54 cm^2
ANSWER:D
Answer: (D) 30.54
Question: Evaluate: 55 - 12*3*2 = ?
(A) 47
(B) 52
(C) 32
(D) 12
(E) 22
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
55 - 12*3*2 = 55 - 8 = 47
correct answer A
Answer: (A) 47
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 352
(B) 350
(C) 3529
(D) 3520
(E) 3501
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: (B) 350
Question: In an increasing sequence of 12 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?
(A) 552
(B) 668
(C) 774
(D) 888
(E) 990
Rationale: let the first term of the sequence be x
since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 12 terms)
now,
sum of first 4 terms =268
or,
4x+16=268
x=252/4=63
Thus the answer can now be calculated by either summing up 63+65+67+... 12th term
or
s=n/2(2a+(n-1)d
=12/2(2*63+(11*2))
=6(126+22)=888
D
Answer: (D) 888
Question: How many consonants are present between the first and sixth vowel in the sequence of English alphabet ?
(A) 12
(B) 13
(C) 11
(D) 10
(E) None of these
Rationale: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
There are only five vowels, hence there are no consonants between first and sixth vowel.
ANSWER E
Answer: (E) None of these
Question: What is the total surface area in square meters of a rectangular solid whose length is 5 meters, width is 4 meters, and depth is 1 meters?
(A) 48 m2
(B) 40 m2
(C) 50 m2
(D) 58 m2
(E) 62 m2
Rationale: Surface Area of a cuboid = 2(lb+bh+lh) = 2(5*4+4*1+5*1)=2(20+4+5)=2*29=58 m2
Answer : D
Answer: (D) 58 m2
Question: Find the odd man out
864, 420, 200, 90, 40, 16, 6
(A) 90
(B) 200
(C) 16
(D) 40
(E) 6
Rationale: 6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on.90
ANSWER:A
Answer: (A) 90
Question: Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
(A) 8
(B) 6
(C) 4
(D) 10
(E) 12
Rationale: Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days.
1/(t+2) + 1/t = 5/12
Now, calculating this is really cumbersome so try to plug in options to get to the answer.
If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4.
1/6 + 1/4 = 5/12
It works so t = 4.
Answer : A
Answer: (A) 8
Question: In a certain quiz that consists of 8 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
(A) 39
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: x
x+4
x+8
x+12
x+16
x+20
x+24
x+28
8x+112=360
8x=248
x=31
3rd question =31+8 = 31+8 = 39
Answer A
Answer: (A) 39
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. Three pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
(A)  5
(B)  12
(C)  24
(D)  32
(E)  120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 24.
Answer: option C
Answer: (C)  24
Question: a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. 3a = b = 3c, and a > 0.
What is the difference between the two greatest possible values of x?
Tip: Dont stop till you have exhausted all answer choices to arrive at the correct one.
(A) 131
(B) 292
(C) 394
(D) 424
(E) 969
Rationale: Ratio of a:b:c= 1:3:1
Two possible greatest single digit values for b are 9 and 6
if b is 9, then x= 393
if b is 6, then x= 262
difference= 393-262= 131
A is the answer
Answer: (A) 131
Question: A man walking at a rate of 5km/hr crosses a bridge in 15 minutes. The length of the bridge is?
(A) 1250m
(B) 1310m
(C) 1500m
(D) 1000m
(E) 1195m
Rationale: Speed = 5*5/18 = 25/18 m/sec
Distance covered in 15minutes = 25/18 *15 *60 = 1250m
Answer is A
Answer: (A) 1250m
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 14 years. The ratio of their ages after 8 years will be
(A) 5 : 3
(B) 8 : 11
(C) 8 : 7
(D) 6 : 5
(E) 3 : 11
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 14
x = 2
Mini’s age = 8 years
And Minakshi’s age = 6 years
Ratio of their ages after 8 years = (8 + 8) : (6 + 8) = 16 : 14 = 8 : 7
ANSWER:C
Answer: (C) 8 : 7
Question: If x is a sum of all even integers on the interval 13...45 and y is their number, what is the GCD (x, y)?
(A)  1
(B)  16
(C)  26
(D)  52
(E)  1014
Rationale: x = 14 + 16 + ... + 44 = (largest + smallest)/2 *(# of terms) = (14 + 44)/2*16 = 29*16.
GCD of 16 and 29*16 is 16.
Answer: B.
Answer: (B)  16
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2445?
(A) s.800
(B) s.810
(C) s.815
(D) s.900
(E) s.920
Rationale: 2445 * 1/3 = 815
Option C
Answer: (C) s.815
Question: 800 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now?
(A) 10
(B) 8
(C) 16
(D) 11
(E) 15
Rationale: 800*20 = 1200*x
x = 16.Answer: C
Answer: (C) 16
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 25%?
(A) 20%
(B) 25%
(C) 13 %
(D) 12.5%
(E) 13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 75
2/3 SP1 = 75
SP1 = 225/2
100 --- 12.5=> 12.50%
ANSWER:D
Answer: (D) 12.5%
Question: The distance between two planets is 3.00 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
(A)  9.3 × 10^5
(B)  9.2 × 10^5
(C)  9.3 × 10^7
(D)  9.9 × 10^7
(E)  10.1 × 10^8
Rationale: 3.00*10^6 light years = 3.00*10^6/3.26 parsecs.
3.00/3.26 is a little bit less than 1, something like 0.9, thus 3.00*10^6/3.26 = ~0.92*10^6 = 9.2*10^5.
Answer: B.
Answer: (B)  9.2 × 10^5
Question: The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.
(A) 33
(B) 77
(C) 48
(D) 99
(E) 61
Rationale: π * 12 * 4 = 48
Answer:C
Answer: (C) 48
Question: The average weight of a group of boys is 35 kg. After a boy of weight 40 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 35x
After the boy weighing 40 kg joins the group, total weight of boys = 35x + 40
So 35x + 40 = 36(x + 1) = > x = 5.
Answer: B
Answer: (B) 5
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 60
(B) 88
(C) 77
(D) 65
(E) 21
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: A
Answer: (A) 60
Question: A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item
(A) Rs. 660
(B) Rs. 760
(C) Rs. 860
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 1200
= 80/100 * 1200
= 960
Option D
Answer: (D) Rs. 960
Question: An alloy is to contain copper and zinc in the ratio 7 : 3. The zinc required (in kg) to be melted with 35 kg of copper, is?
(A) 10 and 2/3
(B) 15
(C) 9 and 2/3
(D) 9
(E) 10
Rationale: Explanation :
7 : 3 : 35 : x
=> 7x = 3 * 35
=> x = (3*35)/7 = 15 Kg.
Hence 15.
Answer : B
Answer: (B) 15
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
(A) 40%
(B) 80%
(C) 58%
(D) 50%
(E) 60%
Rationale: Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
Answer:D
Answer: (D) 50%
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 50%
(C) 57%
(D) 60%
(E) 65%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: If the President and Vice President must sit next to each other in a row with 8 other members of the Board, how many different seating arrangements are possible?
(A) 120510
(B) 632010
(C) 725760
(D) 705262
(E) 851032
Rationale: We need to take President and VP as one unit. Therefore we have 9 people to arrange=5! ways
Also, we both President and VP can be arranged in 2 ! ways.
Reqd no of ways=9!*2!= 725760 ways
Answer C
Answer: (C) 725760
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.204 less than the sum lent. What was the sum lent?
(A) 228
(B) 278
(C) 300
(D) 500
(E) 821
Rationale: P - 204 = (P*4*8)/100
P = 300
Answer: C
Answer: (C) 300
Question: On the xy-coordinate plane, point A lies on the y-axis and point B lies on the x-axis. Points A, B, and C form a right triangle with a 90-degree angle at point C and the triangle has an area of 18. If AC is parallel to the x-axis, and BC is parallel to the y-axis, which of the following could be the coordinates of point C?
(A) (2, -16)
(B) (-5, -8)
(C) (12, 4)
(D) (3, 5)
(E) (9, -4)
Rationale: The area of the triangle formed will be:
1/2 * base * height =
1/2 * |(X-coordinate of point C)| * |(Y-coordinate of point C)| = 18
Thus |product of coordinates of point C| = 36
The answer is E.
Answer: (E) (9, -4)
Question: Product of two natural numbers is 19. Then, the sum of reciprocals of their squares is
(A) 290/289
(B) 1/289
(C) 290/90
(D) 362/361
(E) None of these
Rationale: Explanation:
If the numbers are a, b, then ab = 19,
as 17 is a prime number, so a = 1, b = 19.
1/a2+1/b2=1/1(2)+1/19(2)
=362/361
Option D
Answer: (D) 362/361
Question: 5/8 of 3/10 of a number is greater than 4/9 of 1/4 of the same number by 55. What is half of that number?
(A) 310
(B) 312
(C) 320
(D) 314
(E) 360
Rationale: Let no. be x
5/8*3/10*x - 4/9*1/4*x =55
by further solving
15x/80- 4x/36=55
11x/144=55
x=720
we have to find x/2
=720/2=360
ANSWER:E
Answer: (E) 360
Question: The average of 30 numbers is 48. If three numbers namely 45, 55 and 43 are discarded, the average of remaining numbers is?
(A) 47
(B) 47.03
(C) 48.03
(D) 48
(E) 49
Rationale: Explanation:
Total of 30 numbers = 30 * 48 = 1440
Average o 27 numbers = 1440 - (45 + 55 + 43) / 27
= 48.03
Answer: Option C
Answer: (C) 48.03
Question: If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions R represents the final price of the item?
(A) R=(10,000z + 100z(x – y) – xyz)/10,000
(B) R=(10,000z + 100z(y – x) – xyz)/10,000
(C) R=(100z(x – y) – xyz)/10000
(D) (100z(y – x) – xyz)/10000
(E) 10000 /(x – y)
Rationale: -A-
z=Original Price
x=MU
y=MD
New price with MU:
z(x/100+1)
New price with MD:
z[(x/100+1)(-y/100+1)]
Solvingâ€¦
=z[((x+100)/100)((-y+100)/100)]
=z(x100-xy+10000-100y)/10000
=(zx100-xyz+10000z-100yz)/10000 --> similar to A
Answer: (A) R=(10,000z + 100z(x – y) – xyz)/10,000
Question: If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.67 per litre then what is the rate of mixed oil per litre?
(A) Rs.49.17
(B) Rs.51.03
(C) Rs.54.17
(D) Rs.55.66
(E) None of the above
Rationale: 50*10 = 500
67*5 = 335
835/15 = 55.66
ANSWER:D
Answer: (D) Rs.55.66
Question: List K consists of 10 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 12
Rationale: Answer = A = 5
If least = -3, then largest = 6
Range = 6- 1 = 5
Answer: (A) 5
Question: At a dinner party, 8 people are to be seated around a circular table. Two seating arrangement 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) 5040
(D) 3200
(E) 12000
Rationale: Has to be C.
Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle
hence (8-1)! = 7!= 5040
Answer: (C) 5040
Question: On a certain Monday, Carlos drove to work at an average speed of 20 miles per hour and home from work along exactly the same route at an average speed of 40 miles per hour. Which of the following is closest to his average speed for both trips combined?
(A) 24
(B) 26
(C) 27
(D) 26.66
(E) 28
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/20,
Time in coming back from work = D/40
Hence average speed of both the trips = 2D/ (D/20 + D/40)
= 2*40/3 = 26.66
D
Answer: (D) 26.66
Question: If 5 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
(A) 47.6 kg
(B) 52.6 kg
(C) 59.6 kg
(D) 56.6 kg
(E) 57.6 kilogram
Rationale: (3 * 5)/48 = (9 * 2)/ x
x = 57.6 kg
ANSWER:E
Answer: (E) 57.6 kilogram
Question: Three numbers are in the ratio 3 : 5 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 50. Find the third number?
(A) A)54
(B) B)50
(C) C)48
(D) D)46
(E) E)63
Rationale: Let the numbers be 3x, 5x, 7x.
Largest number = 7x.
Smallest number = 3x.
Third number = 5x.
7x + 3x = 5x + 50
5x = 50 => third number is 50.
Answer:B
Answer: (B) B)50
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) 19828.89
(B) 19828.8
(C) 19828.85
(D) 19828.83
(E) 19828.81
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80.Answer: B
Answer: (B) 19828.8
Question: Find the least number must be subtracted from 105829 so that remaining no.is divisible by 21?
(A) 7
(B) 10
(C) 20
(D) 32
(E) 35
Rationale: On dividing 105829 by 21 we get the remainder 10, so 10 should be subtracted
Answer is B
Answer: (B) 10
Question: A wholesaler makes a 10% commission on the selling price for each bag of cat food it sells. If it sells 100 bags of cat food and makes $160 in commission, what was the selling price of each bag?
(A) $4.00
(B) $4.80
(C) $9.60
(D) $16.00
(E) $32.00
Rationale: Commission per one bag: 160/100=1.6
1.6 = 10% of the selling price
1.6=0.1x
x=16
Answer is D.
Answer: (D) $16.00
Question: If x+y=5z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
(A)  2z+1
(B)  3z
(C)  2z
(D)  z/3
(E)  3z/2
Rationale: Pick any number like X=12, Y=8 and Z= 4 so that X+Y=5Z, now then the arithmetic mean will be (12+8+4)/3=8. Now, just look at the answers and put the value of Z there.
(A) 2.4+1=9, but it should be 8.
(B) 3.4=12,no
(C) 2.4=8, it can be the answer, lets check us the other options
(D) 4/3, no
(E) (3.4)/2=6, no
so the answer will be C..
Answer: (C)  2z
Question: In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.75
(B) 3.75
(C) 4.75
(D) 5.75
(E) 6.75
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 110/40 = 2.75 sec.
Answer: Option A
Answer: (A) 2.75
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 25 people, 8 of whom are females, by how much does the index for the females exceed the index for the males in the group?
(A)  0.05
(B)  0.36
(C)  0.2
(D)  0.25
(E)  0.6
Rationale: Index for females = (25-8)/25 = 17/25 = 0.68
Index for males = (25-17/25 = 8/25 = 0.32
Index for females exceeds males by 0.68 - 0.32 = 0.36
Answer: B
Answer: (B)  0.36
Question: A retail item is offered at a discount of c percent (where c > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of c, would result in the same final price?
(A) p+5/1.05
(B) c/1.05 +5
(C) 1.05c-5
(D) c-5/1.05
(E) 1.05(p – 5)
Rationale: Let x be the price of the item.
Final price after discount and sales tax = x * (1 - c/100) * 1.05
Let d be the percent discount which would result in the same final price.
Then,
x * (1 - c/100) * 1.05 = x * (1 - d/100)
=> 1.05 - 1.05c/100 = 1 - d/100
=> d/100 = 1.05c/100 - .05
=> d = 1.05c - 5
Hence ,option C is correct.
Answer: (C) 1.05c-5
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) 228
(B) 288
(C) 27
(D) 200
(E) 881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.Answer:D
Answer: (D) 200
Question: How many 3 digit numbers are divisible by 6 in all ?
(A) 149
(B) 150
(C) 151
(D) 166
(E) 172
Rationale: Explanation:
Required numbers are 102, 108, 114, ... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then,
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150.
ANSWER IS B
Answer: (B) 150
Question: By how much is 30% of 80 greater than 4/5th of 25 ?
(A) 2
(B) 4
(C) 10
(D) 15
(E) 17
Rationale: Answer
It is (30 x 80)/100 - (4 x 25)/ 5 = 24 - 20 = 4
Correct Option: B
Answer: (B) 4
Question: An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?
(A) 175 seconds
(B) 195 seconds
(C) 155 seconds
(D) 115 seconds
(E) 115 seconds
Rationale: Explanation:
Let the time required by x seconds.
Then, More cloth means More time (Direct Proportion)
So,
0.128 : 1 :: 25 : x => x = {\color{Blue} \frac{25\times 1}{0.128}}
=> x = 195.31
So time will be approx 195 seconds
Answer: B
Answer: (B) 195 seconds
Question: In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions ?
(A) 32
(B) 42
(C) 36
(D) 65
(E) 28
Rationale: Number of ways of arranging the vowels =3P3=3!=6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements =3P3=3!=6.
Total number of ways =(6*6)=36.
Answer is C
Answer: (C) 36
Question: A woman has $133,982 in her savings account. What is the least amount of money (in whole number of dollars) that she must add to her account if she wants to split this money evenly among her Three children?
(A) $1
(B) $11
(C) $3
(D) $2
(E) none
Rationale: To find the least amount the woman should add to her saving account to split the money evenly among her 3 children,
she needs to make the total divisible by 3
Simply add the individual digits of the total = 1+3+3+9+8+2=26
If you add 1 , the number is divisible by 3 (26+ 1)
Correct Option : A
Answer: (A) $1
Question: A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 70, how many questions did Student A answer correctly?
(A) 55
(B) 90
(C) 73
(D) 82
(E) 91
Rationale: let the number of correct responses be x
then the number of incorrect responses =100-x
according to question
x-2(100-x)=70 (subtracting twice of incorrect from correct)
3x=270
x=90
ANSWER:B
Answer: (B) 90
Question: If Tom paid $250 toward buying a brand new oven, which represents 20% of the total cost of the oven, how much remains to be paid?
(A) $1000
(B) $1100
(C) $1050
(D) $1300
(E) $2000
Rationale: Explanation:
Let's start with what the total price of the oven would be. If 20% is equal to $250 then 100% equals $x. We just have to multiply $250 by 5 to get total amount=$1250. Out of this amount we then need to deduct the amount already paid which was $250 so we have $1250-$250=$1000
Answer: Option A
Answer: (A) $1000
Question: Fred purchased an item for $15.00. Fred sees the same item a week later on sale for $12.00. What percentage has the item been marked down from what Fred paid?
(A) 3
(B) 5
(C) 15
(D) 20
(E) 30
Rationale: F.P.=15
S.P.=12
markdown is (1-(S.P./R.P.))*100=(1-(12/15))*100=20%
ANSWER:D
Answer: (D) 20
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 145 days, in how many days can R alone complete the remaining work?
(A) 50 days
(B) 110.6 days
(C) 100 days
(D) 150 days
(E) 80 days
Rationale: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 395 days
P works for 60 days--> 60/200 work done => 30%
Q works for 145 days--> 145/250 work done => 58%
28% work left ... R alone will take 28% * 395 = 110.6 days
Answer is (B)
Answer: (B) 110.6 days