divelab/Sys2Bench huggingface dataset:
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A
Answer: A
Question: mr. depak has $459,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
Options:
A)$0
B)$2
C)$3
D)$4
E)$6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+5+9+7+7+4 = 36
If you add 0 , the number is divisible by 6 (36+ 0)
Correct Option : A
Answer: A
Question: A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84m long and it took 9 seconds in passing him.Find the speed of the train?
Options:
A)6m/sec
B)5m/sec
C)12m/sec
D)7m/sec
E)None
Rationale: Let the length of the train be x m.
then, then train covers x meters in 9 seconds and (x+84)m in 21 seconds.
Therefore, x/9=(x+84)/21 =63m
So, the length of the train=63m
Speed of the train=63/9=7m/sec
Answer: Option D
Answer: D
Question: If A is a positive integer, which of the following must be odd?
Options:
A)A+1
B)A^2+A
C)A^2+A+1
D)x^2−1
E)3x^2−3
Rationale: A. A+1 = can be odd or even. Since O + O =E or E + O = O
B. A^2 + A = A(A+1). Since from the above derivation we already know the term A+1 can be Odd or Even, directly substitute here. A(ODD) = Even (When A is Even) or A(EVEN) = EVEN [When A is ODD]
C. Here's the answer. Since we know the term A^2 + A can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: C
Question: 6, 11, 21, 36, 56, 81, 111, 146, 186, 231 ?
Options:
A)511
B)711
C)811
D)611
E)281
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : E.
Answer: E
Question: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
Options:
A)59
B)11!/(2!*2!*2!)
C)56
D)23
E)11!/(3!*2!*2!*2!)
Rationale: Available letters:
M E D I T R A N (8 letters)
E _ _ R
We have 1 combination for E and 1 combination for R, and also we have 8 combinations for the 2nd letter and 7 combinations for the last letter, so:
E 8 7 R = 1 * 8 * 7 * 1 = 56
ANSWER:C
Answer: C
Question: George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?
Options:
A)2/8
B)3/15
C)2/28
D)3/5
E)15/28
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 8C2 = 8*7/2 = 28
Favorable:
Pick 1 sour out of 3 sour
AND
pick 1 sweet out of 5 sweet.
3C1*5C1=3*5=15
P=15/28
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing sour candy first AND Probability of choosing sweet candy
OR
Probability of choosing sweet candy first AND Probability of choosing sour candy
Answer: E
Answer: E
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)788
C)267
D)266
E)123
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A
Answer: A
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 21 hrs and a machine of type S does the same job in 42 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Type R completes 1/21 of the job each hour.
Type S completes 1/42 of the job each hour.
Together R and S complete 1/21 +1/42 = 1/14 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/14) = 1 job completed
n = 7
The answer is B.
Answer: B
Question: A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow.
Options:
A)32
B)36
C)40
D)44
E)50
Rationale: Explanation :
Explation:
Let length of bridge is X
then middle of bridge is X/2.
and Cow is standing at X/2-5 from the end so
After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side.
So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10
so remaining distance is 10m
the cow is hit before 2m i.e cow covers 8m and train will cover 32 m.
Answer : A
Answer: A
Question: A fort had provision of food for 150 men for 30 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29 1/5
B)24
C)42
D)54
E)48
Rationale: After 10 days : 150 men had food for 20 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 20 : x <=> 125 x x = 150 x 20
=> x =150 x 20/125
=> x = 24.
Correct answer is B
Answer: B
Question: The number of diagonals of a polygon of n sides is given by the formula q=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
Options:
A) 3
B) 5
C) 6
D) 7
E) 8
Rationale: q=n(n-3)
q=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: B
Question: Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)5:1
B)5:5
C)5:7
D)5:4
E)5:2
Rationale: Let the amount lent at 4% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 4/100 x + 10/100 (6000 - x) = 600 - 3x/50
=> 600 - 3/50 x = 450 => x = 2500
Amount lent at 10% = 3500
Required ratio = 2500 : 3500 = 5:7
Answer:C
Answer: C
Question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
Options:
A)12400
B)12800
C)12970
D)13015
E)16000
Rationale: 1212 × 4 + 2 = 5050 × 4 + 2 = 202202 × 4 + 2 = 810810 × 4 + 2 = 32423242 × 4 + 2 = 12970 C
Answer: C
Question: A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?
Options:
A)4 brothers and 2 sisters
B)4 brothers and 3 sisters
C)3 brothers and 3 sisters
D)4 brothers and 5 sisters
E)4 brothers and 6 sisters
Rationale: let no. of girls=g n boys=b
b=g+1 ..........(i) as each boy have equal no. of sisters and brothers and he is not included in brothers.so,1 is for him in g+1.
now ,
b=2(g-1)........(ii) as each girl have g-1 sisters.
solving (i) and(ii) we get g=3 and b=4
ANSWER:B
Answer: B
Question: The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as Old was when Old was three times as old as Young. How old is Old?
Options:
A)23
B)27
C)12
D)43
E)37
Rationale: Explanation:
From the options itself,we can see that option c
old = 30
young = 18
30 + 18 = 48
By reducing this years only by one
Before 6years
old = 24 (half of young)
young = 12 (twice of old)
Answer: C
Answer: C
Question: In a sports club with 80 members, 48 play badminton and 46 play tennis and 7 do not play either. How many members play both badminton and tennis?
Options:
A)23
B)21
C)20
D)26
E)27
Rationale: 48+46=94
but where as total number is 80-7=73
therefore answer is 94-73=21
Hence Answer is B
Answer: B
Question: he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
A)123596
B)1237723
C)123776
D)123728
E)123718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596
ANSWER: A
Answer: A
Question: Combine terms: 6a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b
C)-10a + 22b
D)28a + 30b
E)5a + 30b
Rationale: Solution:
6a + 26b -4b – 16a.
= 6a – 16a + 26b – 4b.
= -10a + 22b.
Answer: (C)
Answer: C
Question: Saturn travels around the Sun at an approximate speed of 5.82 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
Options:
A)30,560
B)31,650
C)32,740
D)33,830
E)34,920
Rationale: The speed is 5.82 miles/s. Then 5.82/0.6 = 9.7 km/s
9.7*3600 = 34,920 kph
The answer is E.
Answer: E
Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for?
Options:
A)10 days
B)12 days
C)15 days
D)20 days
E)18 days
Rationale: Let the total money be $x
A's 1 day work = $ x/21
B's 1 day work = $ x/28
A+B 1 day work = $ x/12
The money is sufficient to pay the wages of both for 12 days
Answer is B
Answer: B
Question: The bear alarm at Grizzly’s Peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. Despite this, the alarm only sounds for three out of four bears that actually appear at the resort. If the alarm sounds, what is the probability that a bear has actually been sighted?
Options:
A) 1/4
B) 3/13
C) 27/52
D) 3/4
E) 10/13
Rationale: How many times the alarm goes off --> 10 false + 3 true
How many of these alarms are true --> 3 true alarms
Therefore, p = true alarms/total alarms = 3/13
Or, we can calculate the p (of alarm sounding but no bear detected, i.e. false alarm),
10 times when the alarm goes off - no bear is seen
13 times in all the alarm goes off
So, 10/13 is the p that alarm is a false alarm
Subtracting 10/13 from 1 is the p that it's a true alarm --> (1-10/13) = 3/13....Answer B
Answer: B
Question: Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number
Options:
A)5
B)15
C)7.5
D)4
E)3
Rationale: Explanation:
Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5
Option A
Answer: A
Question: What is the remainder when 980*1050*880*1010 is divided by 22?
Options:
A)15
B)10
C)12
D)8
E)3
Rationale: OA is 'C'.
OE:
take the remainder from each of 980/22, 1050/22 and so on..
980/22 gives remainder = 12
1050/22 gives remainder = 16
880/22 gives remainder = 0
1010/22 gives remainder = 20
the net remainder is the product of above individual remainders. i.e = 12*16*0*20
break them into pairs 12*16/22 gives remainder 16
and 0*20/22 gives remainder 20
so 16*20/22 gives remainder 12.
Answer: C
Answer: C
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
Options:
A)50
B)60
C)40
D)30
E)25
Rationale: Speed = x/10---1
x+20 km if travelled at 14 km/hr
speed = x+20/14---2
from 1 & 2
x = 50
ANSWER A
Answer: A
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Options:
A)52.3
B)52.2
C)52.1
D)52.5
E)52.4
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80
= 52.5
Answer:D
Answer: D
Question: What is the greatest prime factor of (10!9!) + (10!11!)?
Options:
A)23
B)29
C)31
D)37
E)41
Rationale: 10!9! + 10!11!
= 10!9! (1+10*11)
= 12!11!(111)
= 12!11!(3*37)
The greatest prime factor is 37.
The answer is D.
Answer: D
Question: In a box of 10 pens, a total of 2 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)7/12
B)11/20
C)17/30
D)28/45
E)51/90
Rationale: # defective pens = 2
# good pens = 8
Probability of the 1st pen being good = 8/10
Probability of the 2nd pen being good = 7/9
Total probability = 8/10 * 7/9 = 28/45
The answer is D.
Answer: D
Question: If the probability of rain on any given day in City X is 20%, what is probability that it rains on exactly 3 days in a 4 day period?
Options:
A)16/625
B)8/125
C)6/125
D)4/25
E)3/25
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 1/5*1/5*1/5*4/5 = 4/625
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*4/625 =16/625
The answer is A.
Answer: A
Question: An article is bought for Rs.1280 and sold for Rs.900, find the loss percent?
Options:
A)28%
B)29%
C)16%
D)26%
E)32%
Rationale: 1280 ---- 380
100 ---- ? => 29%
Answer:B
Answer: B
Question: If 41/88 = 0.46590, what is the 77th digit to the right of the decimal point of the fraction?
Options:
A)6
B)2
C)5
D)0
E)9
Rationale: we are not concerned what 41/88 means..
we have to look at the decimal..
0.6590means 0.465909090....
so leaving girst,second and third digit to the right of decimal, all ODD numbered are 0 and all EVEn numbered are 9..
here 77 is odd, so ans is 0
Answer is D
Answer: D
Question: Milk contains 10% water. What content of pure milk should be added to 20 liters of milk to reduce this to 5%?
Options:
A)20liters
B)25liters
C)30liters
D)15liters
E)18liters
Rationale: Quantity of water in 20 liters = 10% of 20 liters = 2 liters
Let x liters of pure milk be added.
Then, 2/(20+x) = 5/100
5x = 100
x=20 liters
Answer is A
Answer: A
Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by ?
Options:
A)25 m
B)75 m
C)85 m
D)05 m
E)15 m
Rationale: Explanation:
A:B = 200 : 169
A:C = 200 : 182
=
=> 182:169
When C covers 182 m , B Covers 169 m
When C covers 350 m , B Covers
=> 325 m
So C beats B by (350 - 325) = 25 m.
Answer: A
Answer: A
Question: A train passes a station platform in 39 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)328
B)279
C)240
D)285
E)231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 15
x + 300 = 585
x = 285 m. Answer:D
Answer: D
Question: The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1950. The perimeter of the plot is?
Options:
A)126
B)156
C)190
D)300
E)260
Rationale: Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1950
X = 70
Required perimeter = 2(70+80) = 300
D
Answer: D
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 2t seconds, then what is the length of the platform?
Options:
A)0.5 L
B)L
C)1.5 L
D)2 L
E)3
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 2t
(L+P) / (L/t) = 2t
P = L
The answer is B.
Answer: B
Question: It takes 2 team of farm workers 12 days to completely prepare a piece of land for planting. if both team of workers were to work separately, one of them can complete the work 10 days earlier than the other, how many days will it take each of them to separately complete the work?
Options:
A)12 and 22
B)11 and 21
C)15 and 25
D)9 and 19
E)20 and 30
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two team of workers would complete a job in 12 days. This means that (individually) each of team would take MORE than 12 days to do the job.
Answers D, A and B are illogical, since the individual times must both be greater than 12 days.
so we can TEST the values for Answers C and E.
Using the values for Answers B and D...
Answer B: (15)(25)/(15+25) = 375/40 = 9.4 This is a match
Answer E: (20)(30)/(20+30) = 12
Final Answer:
E
Answer: E
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $7.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
Options:
A)$4.50
B)$5.10
C)$5.30
D)$7.50
E)$5.60
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 7.80 - 3.20 = 4.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
4.6 = T(5.4x) -> T= (4.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*4.6/5.4 = 7.5
Answer D.
Answer: D
Question: If f(x)= 5x^3- 4x+8 and g(y)= 6y-4, then g(f(x)) =
Options:
A)11x^2+4x+4
B)11x^2-12x+44
C)30x^3-24x+44
D)30x^3+4x+4
E)30x^3-12x+44
Rationale: g(f(x)) = 6(f(x)) -4 = 6(5x^3- 4x+8) - 4 = 30x^3-24x+44 =>C
Answer: C
Question: By selling an article for $195, a person gains $45. What is the gain %?
Options:
A)25%
B)30%
C)50%
D)20%
E)10%
Rationale: S.P. = $195
Gain = $45
C.P. = 195-45 = 150
Gain% = 45/150 * 100% = 30%
Answer is B
Answer: B
Question: Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/5 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?
Options:
A)1/2
B)2/3
C)3/4
D)11/30
E)5/6
Rationale: Because we see H willbring 1/3 of his booksto the new home --> try to pick a number that isdivisible by 3.
Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books
After:
H' = 1/3H = 10 books
M' = 1/5M =12 books
Total = 22 books
M' = 22 = 11/30*60
Ratio: 11/30
Ans:D
Answer: D
Question: A herd of goats consists of A males and B females. In that herd, half of the goats that have horns are females. If C goats of the herd do not have horns, then the total number of male goats in the herd that do NOT have horns, in terms of A, B and C is -
Options:
A)(A−B+C)/2
B)(A−B−C)/2
C)(A+B+C)/2
D)(A+B−C)/2
E)(2A−B+C)/2
Rationale: Male Goats = A
Female Goats = B
1/2 of Horn Goats = Females = x (say)
Therefore, other half will be Male = x
Now, Male Goats without horn = A -x -- (1)
Also, Total Goats without horn = C = (A -x) + (B-x)
or x = (A+B - C)/2
Substituting the value of x in equation (1)
We will have A - x =(A−B+C)/2.
Answer A.
Answer: A
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Mike?
Options:
A)40 kg
B)50 kg
C)65 kg
D)66.5 kg
E)80 kg
Rationale: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Answer: D
Question: Find the value of 3 + 2 • (8 – 3)
Options:
A)25
B)13
C)17
D)24
E)15
Rationale: 3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 * 5
= 3 + 10
= 13
correct answer B
Answer: B
Question: If T = 5/9 * (K - 32), and if T = 35, then what is the value of K?
Options:
A)92
B)95
C)98
D)101
E)104
Rationale: K-32=9T/5
K=9T/5 + 32
K=9(35)/5 + 32 = 95
The answer is B.
Answer: B
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 1/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 10% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
Options:
A)$105
B)b $100
C)c $125
D)d $130
E)e $135
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 1/3*1500 =500 ,Selling amount for 500 cabbage = 500 * 0.5 = $ 250
Remaining were sold at a price equal to 10% less than the price each head sold for on the day before i.e , (90/100)*0.5 = $ 0.45
Hence selling cost for the remaining cabbage = 1000 * 0.45 = $ 450
Total selling cost = 450 + 250 = $ 700
Gross profit = $ 700 - $ 600 = $ 100
Hence Answer is B
Answer: B
Question: If 200 lb of a mixture contain 80% husk and 20% sand. Then how much husk needs to be extracted in order to have 75% concentration of Husk?
Options:
A)1/4
B)20/3
C)1/2
D)40
E)60
Rationale: We need to extract 40 lb of husk.
80 % of 200 = 160
20 % of 200 = 40
Now we have t remove husk to have 75 % of Husk ( key point sand is not supposed to be removed)
Let X be the new quantity after removing husk
So, 40 = 25 % of X
X = 160
Husk will 120 lbs , hence we need to remove 1/4 of the total husk or 40 lbs
ANSWER:D
Answer: D
Question: The rational number for recurring decimal 0.125125.... is:
Options:
A)119/999
B)125/999
C)125/1000
D)125/999
E)None of them
Rationale: 0.125125...
= 0.125
= 125/999
Answer is B.
Answer: B
Question: John has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
Options:
A)201
B)301
C)401
D)101
E)501
Rationale: The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
Answer: B
Question: While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 3° east of north, in what direction was it originally flying?
Options:
A)(a) 30° west of north
B)(b) 30° east of north
C)(c) 22° west of north
D)(d) 22° east of north
E)(e) 5° west of north
Rationale: If after a turn of 25° you are 3°NEast, with a 22° turn you would be perfectly pointing at north. So you were, before the turn, 22° to the other side (West).
Answer C)
Answer: C
Question: Triangle ATriangle B are similar triangles with areas 1536 units square and 2166 units square respectively. The ratio of there corresponding height would be
Options:
A)9:10
B)17:19
C)23:27
D)13:17
E)16:19
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1536/2166
(x^2/y^2)=(16*16*6)/(19*19*6)
(x^2/y^2)=17^2/19^2
x/y=16/19
Ans=E
Answer: E
Question: A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
Options:
A)2 / 3
B)1 / 3
C)3 / 3
D)4 / 5
E)2 / 4
Rationale: Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 and 6 are greater than 2. Hence the probability that the number rolled is an even number greater than 2 is given by
(number of even numbers greater than 2) / 6 = 2 / 6 = 1 / 3
correct answer B
Answer: B