divelab/Sys2Bench huggingface dataset:
Question: Let each different arrangement of all the letters of DELETED be called a word. In how many of these words will the D's be separated?
Options:
A)150
B)200
C)300
D)350
E)400
Rationale: here are 7 letters in the word "DELETED", out of which: D=2, E=3, L=1, T=1.
Total # of permutations is 7!/2!3!=420
# of permutations with D's together is 6!3!=120. Consider 2 D's as one unit: {DD}{E}{E}{E}{L}{T} - total 6 units, out of which {DD}=1, {E}=3, {L}=1, {T}=1.
# of permutations with D's not come together is: 7/2!3!−6!3!=300
ANSWER:C
Answer: C
Question: In a two-digit number, if unit digit exceeds its ten's digit by 2 and the product of the given number and the sum of its digits is equal to 144, then what is the number?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Let the 10's digit be x.Then the units digit will be x+2.
the number is 11x+2.
The sum of the digits will be 2x+2
(11x+2)(2x+2)=144
Solving the quadratic eqn we get x=2;so the number is 24.
ANSWER:D
Answer: D
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)65 cm2
B)30 cm2
C)16 cm2
D)17 cm2
E)15 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x)
= 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle
= 6 * 5 = 30 cm2
Answer: B
Answer: B
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.2
B)10.5
C)10.9
D)10.8
E)10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.Answer: D
Answer: D
Question: The average of 10 members is 15665. If 2 members have 20000 then what is the average of remaining?
Options:
A)12581.25
B)13581.25
C)14581.25
D)15581.25
E)16581.25
Rationale: 20000*2+8*x=15665*10
8x=156650-40000
x=116650/8
x=14581.25
ANSWER:C
Answer: C
Question: How many 5 digit numbers can be formed by using 0,2,4,6,8 which is divisible by 8? (for a no. to be divisible by 8, last three digits of the number should be divisible by 8)
Options:
A)30
B)28
C)26
D)32
E)34
Rationale: 1st place can be filled in 4 no of ways (except 0)
2nd place can be filled in 3 no of ways
last 3 places can be filled in 18 no of ways
total 4*3+18=30
ANSWER:A
Answer: A
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 5 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
Options:
A)11:54:40 AM
B)11:56:24 AM
C)11:40:00 AM
D)11:54:24 AM
E)12:06:36 PM
Rationale: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 32 minutes in 4 days.
Clock gains: 1% in the subsequent 5 days = 1% in 5*24*60 minutes = 72. minute in 5 days;
Net gain in 9 days = 72 - 32 = 40 minutes.
11AM + 40 minutes = 11:40
Answer: C.
Answer: C
Question: √{(2.4)(10^9)} is closest to which of the following?
Options:
A)35,000
B)50,000
C)75,000
D)90,000
E)120,000
Rationale: √{(2.4)(10^9)} = √{(24)(10^8)} = √(24)√(10^8) = (√24) * 10,000 which is almost 50,000.
The answer is B.
Answer: B
Question: From 6 positive numbers and 6 negative numbers, how many groups R of 4 numbers, yielding a positive product, can be formed?
Options:
A)720
B)625
C)30
D)960
E)255
Rationale: Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
R=15 +15 + 15*15 = 255=E
Answer: E
Question: Claire can paint the living room in 7 hours and Barry can paint the living room in 5 hours. How many hours will it take for both of them working together to paint the living room?
Options:
A)2
B)2 11/12
C)3 5/11
D)4 1/2
E)5
Rationale: Work hrs=AB/(A+B)= 35/12 =2 11/12
Answer is B
Answer: B
Question: A man can hit a target once in 4 shots. If he fires 4shots in succession, how many ways that he will hit his target?
Options:
A)71/234
B)81/133
C)81/343
D)81/256
E)91/324
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1414 = 3434
Therefore, the probability that he will not hit the target in any of the four shots = 3434 * 3434 * 3434 * 3434 = 81/256
D
Answer: D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
Options:
A)5336
B)5340
C)5342
D)5345
E)6300
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300.
E
Answer: E
Question: Two persons start running simultaneously around a circular track of length 600 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)11
B)54
C)28
D)27
E)12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 600 / (15 + 25)5/18 = 600* 18 / 40 * 5 = 54 seconds.
Answer: B
Answer: B
Question: If x and y are integers and xy = 330, x or y must be divisible by which of the following?
Options:
A)4
B)6
C)11
D)20
E)30
Rationale: xy = 330 = 2 * 3 * 5 * 11
One of x or y must be divisible by 11.
The answer is C.
Answer: C
Question: The area of a triangle will be when a = 3m, b = 4m, c = 5m, a, b, c being lengths of respective sides?
Options:
A)3
B)6
C)4
D)9
E)1
Rationale: S = (3 + 4 + 5)/2= 6 Answer:B
Answer: B
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
Options:
A)5/11
B)6/11
C)7/11
D)8/11
E)9/11
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
ANSWER:B
Answer: B
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 2 years ago?
Options:
A) 8
B) 10
C) 12
D) 14
E) 16
Rationale: Let's say
Age of Richard isR
Age of David isD
Age of Scott isS
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 2 years ago?
i.e. D-2 = 14-2 = 12 years
Answer: Option
C
Answer: C
Question: Look carefully for the pattern, and then choose which pair of numbers comes next.
28 25 5 21 18 5 14
Options:
A)11 5
B)10 7
C)11 8
D)5 10
E)10 5
Rationale: Explanation: This is an alternating subtraction series with the interpolation of a random number, 5, as every third number. In the subtraction series, 3 is subtracted, then 4, then 3, and so on.
Answer: Option A
Answer: A
Question: A fruit drink is made of orange, watermelon, and grape juice, where 25 percent of the drink is orange juice and 40 percent is watermelon juice. If the drink is made with 105 ounces of grape juice, how many ounces is the drink total?
Options:
A)220
B)250
C)280
D)300
E)340
Rationale: Let the total number of ounces in the drink be x.
% of orange = 25%
% of watermelon = 40%
% of grape = 100% - 65% = 35%
0.35x = 105
x = 300
Therefore there are a total of 300 ounces in the drink.
The answer is D.
Answer: D
Question: In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
Options:
A)330000
B)340000
C)347000
D)356000
E)357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
E)
Answer: E
Question: A sum of money triples itself in twelve years at simple interest. Find the rate of interest?
Options:
A)16 2/7 %
B)16 8/3 %
C)17 2/3 %
D)11 2/3 %
E)16 2/3 %
Rationale: Let the pricipal be Rs. x, then amount = 3x(where R = rate of interest) => Interest = 3x - x = Rs. 2x
R = (100 * 2x)/(x * 12) = 50/3 % = 16 2/3 %.Answer: E
Answer: E
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Options:
A)720
B)850
C)200
D)365
E)750
Rationale: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER A
Answer: A
Question: Five years ago the average of the ages of A and B was 20 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Options:
A)45 years
B)55 years
C)57 years
D)we cannot determined
E)None of these
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 20 => a + b = 50 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
From (1) and (2), we cannot find b.
ANSWER:D
Answer: D
Question: If a boat is moving in upstream with velocity of 14 km/hr and goes downstream with a velocity of 40
km/hr, then what is the speed of the stream ?
Options:
A)13
B)44
C)55
D)6
E)77
Rationale: 13 km/hr
Answer:A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?
Options:
A)299
B)217
C)698
D)277
E)161
Rationale: S.I. for 1 year = (854 - 815) = Rs. 39
S.I. for 3 years = 39 * 3 = Rs. 117
Principal = (815 - 117) = Rs. 698.Answer:C
Answer: C
Question: Evaluate: 1182 - 12*3*2 =?
Options:
A)674
B)574
C)174
D)274
E)374
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
1182 - 12*3*2 = 1182 - 8 = 174
correct answer C
Answer: C
Question: 10 camels cost as much as 24 horses, 26 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.170000, find the cost of a camel?
Options:
A)Rs.6184.5
B)Rs.4184.5
C)Rs.5700
D)Rs.4284.5
E)Rs.5184.5
Rationale: Cost of the camel = P
10 camels = 24 horses
26 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.170000
P = Rs.[(24 * 4 * 4 * 170000)/(10 * 26 * 6 * 10)]
P = Rs.(65280000/15600) => P = Rs.4184.5
ANSWER:B
Answer: B
Question: A driver would have reduced the time it took to drive from home to the store by 1/4 if the average speed had been increased by 12 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
Options:
A)24
B)28
C)32
D)36
E)40
Rationale: Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/4 would give us:
D = (R)(T) = (3T/4)(x*R)
x = 4/3 since (3T/4)(4R/3) = (R)(T) = D
4R/3 = R + 12
R/3 = 12
R= 36
The answer is D.
Answer: D
Question: A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)80
B)90
C)95
D)98
E)102
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 544
16x = 544
x = 34.
Hence, total number of notes = 3x = 102
E
Answer: E
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)27 7/8
B)27 7/6
C)27 7/4
D)27 7by9
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D
Answer: D
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability M that one more throw to this series will increase the mean score?
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability Mis 1/2.C
Answer: C
Question: The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?
Options:
A)75 kg
B)65 kg
C)55 kg
D)85 kg
E)25 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer: D
Answer: D
Question: A restaurant meal cost $30.5 and there was no tax. If the tip was more than 20 percent but less than 30 percent of the cost of the meal, then the total amount paid must have been between
Options:
A)$40 and $42
B)$39 and $41
C)$38 and $40
D)$37 and $39
E)$36 and $39
Rationale: The total amount for the meal was between 30.5*1.2=36.6 and 30.5*1.3=~39.65. Only option which covers all possible values of the meal is D.
Answer: D.
Answer: D
Question: If the average of 9 consecutive number is T. How much will the average increase by if the next 3 consecutive numbers are also added?
Options:
A)3
B)1.5
C)2.5
D)Can’t be determined
E)None of these
Rationale: DETAILED SOLUTION
Let the numbers be n, n+1, n+2……………….n+8
Average of these numbers = n + 4
When n +9, n+10, n+11 are added, the difference of these numbers from the earlier average = 5, 6, 7 respectively = 18
This 18 will increase the average by 18/15 = 1.5
CORRECT ANSWER B
Answer: B
Question: Two pipes A and B can fill a tank in 40 and 120 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A)30
B)35
C)25
D)82
E)22
Rationale: Part filled by A in 1 min. = 1/40
Part filled by B in 1 min. = 1/120
part filled by (A + B) in 1 min. = 1/40 + 1/120 = 1/30.
Both the pipes can fill the tank in 30 minutes.
Answer: A
Answer: A
Question: 100 oranges were bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. What is the percentage of profit or loss?
Options:
A)19 2/7%
B)17 2/7%
C)14 2/7%
D)15 2/7%
E)5 15/17%
Rationale: 100*48/12*350-1)100=1/7*100=14 2/7%
i.e., profit percentage =14 2/7%
Answer : C
Answer: C
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is?
Options:
A)2987
B)2000
C)2789
D)7999
E)7389
Rationale: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse
= Rs.2000.
Answer: B
Answer: B
Question: The monthly salaries of six employees in a company are $1000, $2500, $3100, $3650, $1500, $2000. What is the mean of the salaries of 6 employees.
Options:
A)$2291.7
B)$1546.8
C)$2546.5
D)$1879.3
E)$3125.3
Rationale: mean of the salaries = ($1000+ $2500+ $3100+ $3650+ $1500+ $2000)/6 = 13750/6 = $2291.7
Answer is A
Answer: A
Question: If q and d are both integers, q>d, and -3q>19, then the largest value of d would be?
Options:
A)-5
B)-6
C)-7
D)-8
E)-10
Rationale: No, your thinking is incorrect. When we know that q>d and q<-6.33, the largest value of q can be -7 while if q=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<q and q = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: D
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 7/4 of her salary.What fraction of her income for the week came from tips?
Options:
A)1/9
B)1/6
C)2/3
D)4/9
E)7/11
Rationale: Her tips were 7/4 of her salary.
Let's say her salary =$4
This mean her tips = (7/4)($4) =$7
So, her TOTAL INCOME =$4+$7=$11
What fraction of her income for the week came from tips
$7/$11= 7/11
= E
Answer: E
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 800 per sq. metre.
Options:
A)Rs. 15000
B)Rs. 15550
C)Rs. 15600
D)Rs. 16500
E)None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (800 × 20.625) = 16500. Answer D
Answer: D
Question: How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARIT', if repetition of letters is not allowed?
Options:
A)690
B)210
C)740
D)760
E)780
Rationale: The word 'LOGARIT' has 7 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 7P3
=
7
×
6×
5
=
210
Option B
Answer: B
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
A)1
B)2
C)5
D)6
E)8
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Answer: B
Question: . A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit . For how long B’s money was used.
Options:
A)33
B)27
C)10
D)8
E)82
Rationale: Explanation:
B received 2/3 of the profit ⇒Their profits ratio = A : B = 1 : 2
Let the total capital = 4 units
Then A's capital = 1
B's capital = 3
Assume B's money was used for b months
Then A : B = 1 × 15 : 3 × b = 1 : 2
⇒ 15 : 3b = 1 : 2
⇒ 153b=12153b=12
⇒ b = 10
Answer: C
Answer: C
Question: Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ?
Options:
A)97.959%
B)98.959%
C)99.959%
D)96.959%
E)95.959%
Rationale: let the number be x
the right number is 7x
the wrong number is x/7
error is(7x-x/7)=48x/7
percentage of error is((48x/7)/7x)*100=97.959%
ANSWER:A
Answer: A
Question: A certain ski shop sells pairs of gloves in 9 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
Options:
A)1/144
B)1/143
C)1/24
D)1/23
E)1/17
Rationale: there are 9 different colours sothere are 9 pairs of gloves dropped..
first can be any of 18..so 18/18..
second has to be its pair, which will be just one out of remaining 17.. 1/17..
overall prob=18/18*1/17= 1/17..
E
Answer: E
Question: If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph,then the man’s rate along the current is :
Options:
A)4.25 kmph
B)6 kmph
C)6.5 kmph
D)8.5 kmph
E)None of these
Rationale: Solution
Let the rate along the current be x kmph.Then,1/2(x + 3.5) = 5 or x = 6.5 kmph. Answer C
Answer: C
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 15 percent of the test takers answered neither question correctly, what percent answered both correctly?
Options:
A)60 %
B)65 %
C)70%
D)75%
E)80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 75 - {Both correctly} + 15
{Both correctly} = 75.
Answer: D.
Answer: D
Question: The unit digit in the product (635 * 767 * 984 * 489) is:
Options:
A)0
B)8
C)3
D)2
E)1
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (5*7*4*9) = 0
ANSWER: A
Answer: A
Question: If b does not equal zero, and ab = b/8, what is the value of a?
Options:
A)A)1/8
B)B)1/4
C)C)1/3
D)D)1/2
E)of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/8
(ab)/b = (b/8)/b
a = (b/8)*1/b
a = 1/8
Answer: (A).
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)11
B)22
C)44
D)55
E)79
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer:C
Answer: C
Question: The average weight of 8 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)kg
B)70 kg
C)80 kg
D)90 kg
E)93 kg
Rationale: Total weight increased = (8 x 3.5) kg = 28 kg.
Weight of new person = (65 + 28) kg = 93 kg.
E)
Answer: E
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 80 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?
Options:
A)110
B)112
C)116
D)118
E)122
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(4x/5) is an integer
Or x/5 is an integer.
Hence we need the lowest multiple of 5 from the given options.
Let us start from the lowest value:
Option A: 110. This is a multiple of 5 Hence the correct answer.
Correct Option: A
Answer: A
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 70% of Mary and John’s combined income?
Options:
A) $3,000
B) $4,000
C) $7,000
D) $11,000
E) $27,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (70/100)* (15,000 + x + 18000 )
15,000 + x = (14/20) * (33,000 + x)
300,000 + 20x = 14x + 462,000
6x = 162,000
x = 27,000
So, Answer will be E
Answer: E
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)610
B)720
C)825
D)920
E)None of these
Rationale: Explanation :
The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels
should always come together. Hence these three vowels can be grouped and considered as a
single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5. and all these letters are different.
Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120
All The 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6
Hence, required number of ways = 120 x 6 = 720. Answer : Option B
Answer: B
Question: A rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
Options:
A)46m
B)26m
C)26m
D)56m
E)25m
Rationale: Perimeter of the plot = 2(15+50) = 130m
no of poles =130/5 =26m
Answer: B
Answer: B