divelab/Sys2Bench huggingface dataset:
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 24 minutes is:
Options:
A)9
B)5
C)7
D)6
E)10
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(24/60)) km = 10 km.
ANSWER:E
Answer: E
Question: Average monthly income of a family of 4 earning members was Rs. 840. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?
Options:
A)Rs. 692.80
B)Rs. 820
C)Rs. 990
D)Rs. 1410
E)None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 840 x 4 - 650 x 3 Rs.
= 1410 Rs.
Correct Option: D
Answer: D
Question: The G.C.D of 1.08, 0.36 and 0.9 is
Options:
A)0.19
B)0.1
C)0.18
D)0.11
E)0.12
Rationale: Explanation:
Given numbers are 1.08 , 0.36 and 0.90
H.C.F of 108, 36 and 90 is 18 [ \inline \fn_jvn \because G.C.D is nothing but H.C.F]
\inline \fn_jvn \therefore H.C.F of given numbers = 0.18
Answer: C) 0.18
Answer: C
Question: Express of the following as a fraction: 4%
Options:
A)2/25
B)1/25
C)4/25
D)7/25
E)None of them
Rationale: 4% =4/100 =1/25.
Answer is B.
Answer: B
Question: A 40-liter solution of alcohol and water is 5 percent alcohol. If 3.5 liters of alcohol and 6.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Options:
A)8%
B)11%
C)14%
D)17%
E)20%
Rationale: The percent of alcohol in the solution is (0.05(40) + 3.5) / 50 = 5.5/50 = 11%
The answer is B.
Answer: B
Question: The rate of Interest on a sum of money is 3% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occurred on the sum for the total period of 8 years is Rs. 540/-, the sum is
Options:
A)1,200
B)1,800
C)2,100
D)2,250
E)2,540
Rationale: Explanation:
I1 = (P x 3 x 3)/100 = P/11
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
P/11+ 4P/25 + P/20 = 540
30P/100 = 540
P = 1800
Answer: Option B
Answer: B
Question: If 7 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
Options:
A)21
B)42
C)43
D)44
E)45
Rationale: n(n-1)/2 =7*6/2
=21
ANSWER:A
Answer: A
Question: A freight elevator can carry a maximum load of 1150 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
Options:
A)42
B)85
C)190
D)215
E)210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1150 - 200 - 430 = 520.
allowed per package = 520 / 3 = 173
So difference in average of existing and allowable = 215 - 173 = 42
Hence A
Answer: A
Question: A is twice as good a work man as B and together they finish the work in 8 days. In how many days A alone can finish the work?
Options:
A)23
B)12
C)77
D)92
E)61
Rationale: WC = 2:1
2x + x = 1/8 => x = 1/24
2x = 1/12
A can do the work in 12 days.
Answer: B
Answer: B
Question: In a garden, there are five blue flowers, five red flowers, five green flowers, and five pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
Options:
A)11/10
B)6/55
C)31/10
D)3/55
E)1/16
Rationale: P(all the same color) = P(1st flower is ANY colorAND2nd flower is same as firstAND3rd flower is also the same color)
= P(1st flower is ANY color)xP(2nd flower is same as 1st)ANDP(3rd flower is the same color)
= 1x4/11x3/10
= 6/55
Answer: B
Answer: B
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 120?
Options:
A)3
B)14
C)32
D)30
E)70
Rationale: Greatest common factor n and 16 is 4 = 2*2 * 2*2
Greatest common factor n and 45 is 3 = 3*3 *5
Greatest common factor n and 120 is = 2*3*5 =30
Answer: D.
Answer: D
Question: JERRY has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If JERRY needs to pay exactly $128, what is the least number of bills he will need to use?
Options:
A)16
B)35
C)46
D)577
E)576
Rationale: 128 is the total sum of money.
as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils
128-120 = 8
so now we need to get 8 from either 5 dollar bills or 1 dollar bills
8 - 5 (use only 1 5 dollar bill) = 3
so we can get 3 from using 3 $1 bills.
Hence 16 ( 12+1+3 )
ANSWER IS A
Answer: A
Question: What percent of 7.2 kg is 18 gms ?
Options:
A)25
B)66
C)288
D)19
E)17
Rationale: Explanation:
Required percentage = (18/7200 * 100)% = 1/4% = 0.25%
Answer: A) .25%
Answer: A
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.30 m space around the room. A side of square tile is given to be 20 cms?
Options:
A)187
B)714
C)268
D)208
E)276
Rationale: Area of the room =3.4 * 8.4 = 28.56
Area of the tile = 0.2 *0.2=0.04
No. of tiles = 28.56/0.04 =714
Answer : B
Answer: B
Question: In the graph below, no axes or origin is shown. If point B's coordinates are (10,5), which of the following coordinates would most likely be A's?
Options:
A)(17, -2)
B)(10, 6)
C)(6, 8)
D)(-10, 3)
E)(-2, -17)
Rationale: wherever be the axis as per question y coordinate of point A will be greater than 3 and X coordinate will be lower than 10.
E rules..
Answer: E
Question: Sobha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Options:
A)4
B)6
C)8
D)10
E)2
Rationale: Age of Sobha's father when Sobha was born =38
Age of Sobha's mother when Sobha was born =36−4=32
Required difference of age =38−32=6
Answer is B.
Answer: B
Question: Calculate the distance covered by 200 revolutions of a wheel of radius 21 cm.
Options:
A)1164 m
B)664 m
C)364 m
D)164 m
E)264 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 200 * 2 * 22/7 * 21 = 26400 cm = 264 m
ANSWER:E
Answer: E
Question: Find large number from below question The difference of two numbers is 1311. On dividing the larger number by the smaller, we get 11 as quotient and the 11 as remainder
Options:
A)1209
B)1324
C)1441
D)1300
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1311).
x + 1311 = 11x + 11
10x = 1300
x = 130
Large number = 130+1311 = 1441
Answer : C
Answer: C
Question: If a*b*c=65, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?
Options:
A)1/2
B)1/4
C)3/4
D)2/3
E)None of these
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 65/65 => a/d = 1
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/1000 => f/c = 1/4
a/d* f/c = 1 * 1/4 = 1/4
Answer : B
Answer: B
Question: The average mark of the students of a class in a particular exam is 80. If 8 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
Options:
A)15
B)25
C)35
D)45
E)56
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 8) students = 90(x - 8)
80x - (8 * 20) = 90(x - 8)
560 = 10x => x = 56
ANSWER:E
Answer: E
Question: The price of rice falls by 25%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
Options:
A)5 kg
B)15 kg
C)26.67 kg
D)30 kg
E)None
Rationale: Solution: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 -25% of 100) = 75
New price of rice = 75/20 = Rs. 3.75 per kg.
Rice can bought now at = 100/3.75 = 26.67 kg.
Answer: Option C
Answer: C
Question: A boat can move upstream at 46 kmph and downstream at 64 kmph, then the speed of the current is?
Options:
A)5
B)6
C)9
D)4
E)2
Rationale: US = 46
DS = 64
M = (64 - 46)/2 = 9 Answer:C
Answer: C
Question: 49 Ã— 49 Ã— 49 = 7^?
Options:
A)4
B)7
C)8
D)6
E)None of these
Rationale: 49 Ã— 49 Ã— 49 = 7?
or, 7(2) Ã— 7(2) Ã— 7(2) = 7?
or 7(6) = 7? or, ? = 6
Answer D
Answer: D
Question: In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent thus he secured 41% votes of the total voters on the voter list. Percentage votes of the defeated candidate out of the total votes casted is:
Options:
A)22
B)389
C)38
D)45
E)01
Rationale: Let there be x voters and k votes goes to loser then
0.8x - 120 = k + (k + 200)
k+200 = 0.41x
\inline \Rightarrow k = 1440
and (k + 200) =1640
Therefore \inline \frac{1440}{3200}\times 100 = 45%
Answer: D) 45%
Answer: D
Question: Lloyd normally works 7.5 hours per day and earns $4.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 2.0 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)$47.25
C)$60.75
D)$54.00
E)$70.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*4.5+ 3*4.5*2.0=60.75
Answer C
Answer: C
Question: A cylindrical cube of radius 12 cm contains water upto a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. The radius of the ball is :
Options:
A)7 cm
B)8.5 cm
C)9 cm
D)9.5 cm
E)None
Rationale: Sol.
Let the radius of the ball be r cm.
Volume of ball = Volume of water displaced by it.
∴ 4/3 ∏r³ = ∏ * 12 * 12 * 6.75
⇒ r³ = 9 * 9 * 9 ⇒ r = 9 cm.
Answer C
Answer: C
Question: 9 examiners can examine a certain number of answer books in 12 days by working 5 hours a day. How many hours in a day should 4 examiners work to examine twice the number of answer books in 30 days?
Options:
A)9
B)10
C)11
D)12
E)15
Rationale: Explanation:
Let required number of hours be x
More examiners, less hours (indirect proportion)
More days, less hours (indirect proportion)
More answer books, more hours (direct proportion)
Hence we can write as
(examiners) 9:4
(days) 12:30
(answer books) 2:1 }::x:5
⇒9×12×2×5=4×30×1×x
⇒x=9×12×2×5/4×30×1
=9×3×2×5/30
=9×2×5/10
=9
Answer: Option A
Answer: A
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)5 min
B)2 min
C)6 min
D)10 min
E)3 min
Rationale: Explanation:
Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =(9/24*60)=10 min
ANSWER:D
Answer: D
Question: what is the least number. which should be added to 0.0478 to make it a perfect square?
Options:
A)0.0002
B)0.0004
C)0.0006
D)0.0008
E)0.001
Rationale: 0.0478+0.0006=0.0484
(0.22)^2
ANSWER:C
Answer: C
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)355
Rationale: Clearly, the numbers are (23 x 13) and (23 x 15).
Larger number = (23 x 15) = 345. Answer: Option D
Answer: D
Question: A painting 2 inches wide is placed around a rectangular board with dimensions 8 inches by 12 inches. What is the area of the painting, in square inches?
Options:
A)144
B)196
C)96
D)144
E)128
Rationale: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a painting 2 inches wide is placed around a rectangular board with dimensions 8 inches by 12 inches. We're asked for the area of the painting , in square inches.
Area of a rectangle = (length)(width)
So the area of the board is... (8)(12) = 96
The painting 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...
(8+2+2)(12+2+2) = (12)(16) = 196
When we 'punch out' the area of the rectangular board , we'll be left with the area of the FRAME:
192 - 96 = 96
Final Answer:
C
Answer: C
Question: A can do a work in 10days and B can do the same work in 8 days. They work together for 3days and then A goes away. In how many days will B finish the work?
Options:
A)11/17days
B)21/40days
C)31/40days
D)14/21days
E)15/31days
Rationale: A+B can do the work in 3 days = 3( 1/10 + 1/8) = 9/40
Rest of the work = 1 - 9/40 = 31/40
B will do the rest of the work in = 1 - 9/40 = 31/40days
Answer is C
Answer: C
Question: Ron has a cycle worth $ 1800 and he wants to sell it at a profit of $ 220. What should cycles selling price be?
Options:
A)2690
B)1790
C)1890
D)2020
E)2300
Rationale: Cost Price = $ 1800
Profit = $ 220
Selling Price = Cost Price + Profit
Selling Price = 1800 + 220
= $ 2020
Selling price of the cycle = $ 2020 ANSWER : D
Answer: D
Question: Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A)2443200
B)3643200
C)5443200
D)1443200
E)2163200
Rationale: Of the six-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7ways;
Choosing the digit for s - 6ways;
Choosing the digit for t - 5ways;
# of permutations of 3 digits in ppqrst - 6!/2!
Total: 9*8*7*6*5*6!/2!=5443200.
Answer: C.
Answer: C
Question: A certain sum of money at simple interest amounted Rs.980 in 3 years at 5% per annum, find the sum?
Options:
A)867
B)855
C)299
D)852
E)903
Rationale: 980 = P [1 + (3*5)/100]
P = 852
Answer: D
Answer: D
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)2000
B)2500
C)2400
D)2600
E)1500
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
ANSWER A
Answer: A
Question: If 6^e is a factor of (10!)^2, What is the greatest possible value of e ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: e 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: D
Question: A salt manufacturing company produced a total of 2500 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
Options:
A)100
B)105
C)109
D)120
E)90
Rationale: Total production of salt by the company in that year = 2500 + 2600 + 2700 + .... + 3600 = 36600.
Average monthly production of salt for that year = 36600/365 â‰ˆ 100
ANSWER:A
Answer: A
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
Options:
A)2,420
B)6,435
C)12,100
D)12,870
E)25,740
Rationale: Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option A is the correct answer..
OA please...will correct if I missed anything..
Answer: A
Question: A certain kind of necklace is made from 9 gold, 6 blue, and 3 white beads. What is the maximum number of these necklaces that can be made from 36 beads of each color ?
Options:
A)8
B)4
C)6
D)5
E)4
Rationale: Atleast 9 gold breads are needed to make a necklace, so irrespective of the combinations of blue and white beads, the number of necklaces that can be formed will be
36/9 =4
Answer:- E
Answer: E
Question: A ladies hostel had provision of food for 200 women for 35 days. After 10 days, 25 women left the hostel. The number of days for which the remaining food will last is:
Options:
A)28.97
B)28.0
C)28.47
D)27.47
E)29.47
Rationale: Explanation :
After 10 days : 200 women had food for 25 days.
Suppose 175 women had food for x days.
Now, Less women, More days (Indirect Proportion)
175 : 200 :: 25 : x
=> 175 x x = 200 x 25
=> x = 200 x 25 / 175
=> x =28.47
Answer : C
Answer: C
Question: A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 3 music tunes of the same type (1 in _____ ) ?
Options:
A)3
B)9
C)8
D)4
E)5
Rationale: 1/2^3=1/8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2*1/8= 1/4 so ans is 4
ANSWER:D
Answer: D
Question: Average of 10 matches is 34, How many runs one should should score to increase his average by 5 runs.
Options:
A)A)70
B)B)76
C)C)78
D)D)89
E)E)88
Rationale: Explanation:
Average after 11 innings should be 39
So, Required score = (11 * 39) - (10 * 34)
= 429 - 340 = 89
Answer: Option D
Answer: D
Question: If x and y are integers, then xy(x + y) is
Options:
A)Always positive
B)Always negative
C)Positive when x is positive
D)Negative when x is negative
E)It cannot be determined by the information given
Rationale: If you consider the case where x = 0 or y = 0, the result is zero regardless of the value (be it positive or negative) of the other variable.
so given that x < 0 (i.e, x is negative) and y = 0, the result = 0.
Answer is E
Answer: E
Question: How many seconds will a 400 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 30 km/hr?
Options:
A)25
B)30
C)45
D)64
E)60
Rationale: Explanation :
Speed of train relatively to man = ( 30 - 6)km/hr
= 24 km /hr
= (24 x 5 / 18)m/sec
= 6.66 m/sec
Time taken to pass the man = (400/ 6.66)sec = 60 sec.
Answer : E
Answer: E
Question: Let x be a positive integer, what is the remainder when 4^(2x+5)+3 is divided by 5?
Options:
A)2
B)3
C)4
D)1
E)5
Rationale: For: (4^(2x+5)+3)/5
Let n = 2x + 5
4^n
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256, last digit pattern repeats 4, 6, 4, 6, ....
Rule: x^(m+n) = (x^m)(x^n)
(4^(2x))(4^5)
Rule: x^(mn) = (x^m)^n
(4^2)(4^x)(4^5) => Now, (6)(4)(4) + 3 = (6) + 3 => Finally, 9/5 and remainder is 4.
Answer: C
Answer: C
Question: Find the L.C.M of 36,90,210
Options:
A)630
B)2520
C)1260
D)1360
E)1460
Rationale: 36=2^2*3^2 90=3^2*2*5 210=2*5*3*7
L.C.M=2^2*3^2*5*7=1260
Answer=(C)
Answer: C
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 150,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
Options:
A)77,500
B)1,860,000
C)2,400,000
D)3,720,000
E)4,960,000
Rationale: 150,000 × 2 × 2×2×2 = 150,000 × 16 = C
Answer: C
Question: The value of y^2+2y-(2yy) when y=3 is:
Options:
A)-2
B)-3
C)4
D)-1
E)2
Rationale: 3^2+2*3-(2*3*3)
9+2*3-(18)
9+6-18
15-18=-3
answer B
Answer: B
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.75
B)5.7
C)5.76
D)5.71
E)5.74
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: C
Question: The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?
Options:
A)11
B)27
C)21
D)92
E)20
Rationale: Explanation:
Let the cost of each pen and pencil be 'p' and 'q' respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 20
Answer: E
Answer: E
Question: list of salaries of 7 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $30,000, $27,000, $32,000
Options:
A)$28,000
B)$28,500
C)$30,200
D)$31,000
E)$31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000
Since there is an odd number of items in the data set, we compute the median by taking the middle number
The median salary is $31,000.
Answer : D
Answer: D
Question: The flying acrobatic team is made up of 120 airplanes. The team wants to form 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 4 and no more than 30, how many different combinations of rectangular shapes are possible?
Options:
A)4.
B)5.
C)6.
D)8.
E)10.
Rationale: firstly factors of 120 = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,... etc...
the questions says each row will have airplanes not less than 4 and not more than 30,
therefore, we should be interested in the factors starting from 4 till 30 (inclusive)
4(in each row) * 30(number of columns) =120, similarly
5 * 24
6 * 20
8 * 15
10 * 12
12 * 10
15 * 8
20 * 6
24 * 5
30 * 4
total possibilities = 10
option E
Answer: E
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)219 sq.units
C)287 sq.units
D)216 sq.units
E)289 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10
= 140 sq.units
Answer: A
Answer: A
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many T kilometers per hour did Tammy walk on the second day?
Options:
A)3
B)3.5
C)4
D)4.5
E)6
Rationale: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Answer: C
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.5, 0.2, and 0.3 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
Options:
A)0.06
B)0.12
C)0.21
D)0.29
E)0.28
Rationale: The probability that eachdoesn'thit is: 0.5, 0.8, and 0.7. When we have multiple independent events, we multiply the probabilities:
.5*.8*.7 = 0.28.
Option: E
Answer: E
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2134
B)2234
C)2540
D)2560
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E