These may be the lousy way to solve the questions, but this is how I attempted to solve the questions.
The
answers may be incorrect. I didn't match them with OA.
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New questions:
1. When the positive integer x is divided by 4, is the remainder equal to 3?
(1) When x/3 is divided by 2, the remainder is 1.
(2) x is divisible by 5.
Soln:
Q: will "x/4" leave a remainder of 3?
(1) Rephrase: (x/3)/2= x/6 leaves remainder 1.
Values of x: 1,7,13,19
x%4 : 1,3 Remainder may be 3 or NOT 3. Not Sufficient.
(2) x%5 = 0
Values of x: 5,10,15
x%4 : 1,2,3 Remainder may be 3 or NOT 3. Not Sufficient.
Both:
Values of x: 25,55,85,115
x%4 : 1,1,1,3 Remainder may be 3 or NOT 3. Not Sufficient.
Ans: "E"
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2. In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?
(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.
(2) It sold each computer for $1000.
Q: What is ratio of: (total money received by selling computers)/(total money received by selling printers)
(1) It just talks about the ratio of number of computers sold. Doesn't talk about how much was it sold for. Not Sufficient.
(2) How many computer and how about the printer!! Not sufficient.
Both: Not sufficient
Ans: "E"
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3. Last Tuesday a trucker paid $155.76, including 10 percent state and federal taxes, for diesel fuel. What was the price per gallon for the fuel if the taxes are excluded?
(1) The trucker paid $0.118 per gallon in state and federal taxes on the fuel last Tuesday.
(2) The trucker purchased 120 gallons of the fuel last Tuesday.
1.1x=155.76
x=(155.76/1.1)
x- base price paid for the entire purchase of the fuel without any taxes- known value
(155.76/(1.1*10)) paid in the taxes
(1) (155.76/(1.1*10))/n=0.118
Number of gallons n can be found. Then x/n to find the price/gallon without taxes. Sufficient.
(2) (155.76/20)*0.9 will be the price per gallon without taxes. Sufficient.
Ans: "D"
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4. What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.
Same approach as question 1. I couldn't find any shortcuts for this.
1.
x -> 5,17,29,41,53,65
x%8 -> 5,1,5,1,5,1. Can be 1 or 5. Not sufficient.
2.
x -> 11,29,47,65
x%8 -> 3,5,7,1 Can be many remainders. Not sufficient.
Both:
x -> 29,65
x%8 -> 5,1. Can be many remainders. Not sufficient.
Ans: "E"
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5. Al, Pablo, and Marsha shared the driving on a 1500 mile trip, which of the three drove the greatest distance on the trip?
(1) Al drove 1 hour longer than Pablo but at an average of 5 miles per hour slower than Pablo.
(2) Marsha drove 9 hours and averaged 50 miles per hour
Total distance: 1500 miles
(1) Al: Drove some miles driving for t hours at k miles/hour of speed
Pablo: Drove some miles for t-1 hours (K+5) miles/hour of speed
Miles driven by Al: tk
Miles driven by Pablo: (t-1)(k+5)
Can't deduce anything beyond this.
Not sufficient.
(2) Marsha drove 9*50=450 miles
So Al+Pablo drove=1050
Definitely, Marsha didn't drive the maximum. Because, Al or Pablo could have driven around 1049 miles alone. Even if equally, they must have
driven 1050/2=525 each, which is > 450. Not sufficient.
Both:
Marsha drove 450 miles
Al + Pablo drove 1050 miles
tk + (t-1)(k+5) = 1050
We can't derive exactly who drove how much of distance. Not sufficient.
Ans: "E"
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6. How many perfect squares are less than the integer d?
(1) 23 < d < 33
(2) 27 < d < 37
(1) d could be 24 or 26
if d=24. Number of Perfect squares less than 24: 1^2=1, 2^2=4, 3^2=9, 4^2=16 = 4
if d=26. Number of Perfect squares less than 26: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5
Not sufficient.
(2) 27 < d < 37
d can be any integer from 28 to 36, inclusive.
from 28 to 36; the number of perfect square less than the number will always be 5.
if d=28. Number of Perfect squares less than 26: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5
if d=36. Number of Perfect squares less than 36: 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 = 5
The question is trying to trick us by saying less than rather than "less than equal to".
We should not count 36 as the perfect square because 36 is not less than 36. It is equal to 36.
Sufficient
Ans: "B"
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7. The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1.
(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.
(1) m and p must both be even
since p is not a multiple of m, remainder can't be 0.
Can it be 1.
For the remainder to 1, p will have to be odd, which is not possible.
So, the remainder will always be more than 1.
Sufficient.
(2) Possible values for m and p are
2,15 -> Remainder: 1 Ans: No
3,10 -> Remainder: 1 Ans: No
5,6 -> Remainder: 1 Ans: No
It can't be 1,30 because 30 is a multiple of 1.
Sufficient.
Ans: "D"
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8. A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?
(1) Since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.
(1) We can infer that bacteria is doubling every 2 hours. So,
2x: two hours back
4x: now
4x-2x=3750
2x=3750
x=1875
r = 2
A = 1875
n = 4
A(5) = a*r^(n-1)
or
simply: 3750*2=now
in 2 hours: 3750*2*2
in 4 hours: 3750*2*2*2
Sufficient
2) I am not too sure what this statement is trying to say. However, here's an abortive effort.
Say, it is time=1:00PM now
We have to consider the time until 1+4=5:00PM
It is saying that from "t+4-1" or from 4:00PM to 5:00PM, the bacteria will grow from 20,000 to 40,000. This is kind of too straightforward to be
true.
In other words, it is(or is it) saying that bacteria's count will be 40,000 when scientist destroys the sample.
Sufficient
Ans: "D"
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9. Is x^2 equal to xy?
(1) x^2 - y^2 = (x+5)(y-5)
(2) x=y
(1) Following values satisfy the equation.
x=y=-5
x=y=5
Can't think of any other number. But, I feel this is a lame way to solve this even if this is true.
Sufficient.
(2) Sufficient.
Ans: "D"
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10. A number of oranges are to be distributed evenly among a number of baskets. Each basket will contain at least one orange. If there are 20 oranges to be distributed, what is the number of oranges per basket?
(1) If the number of baskets were halved and all other conditions remained the same, there would be twice as many oranges in every remaining basket.
(2) If the number of baskets were doubled, it would no longer be possible to place at least one orange in every basket.
Possibilities
basket<->oranges/basket
20<->1
1<->20
10<->2
2<->10
4<->5
5<->4
(1)
Consider
20<->1
Basket halved: 10
Oranges doubled: 2
Consider
10<->2
Basket halved
5<->4
So answer could be 20 or 2. Not sufficient.
(2)
Means after doubling the basket count, it will be more than 20.
Possible only in 20<->1 scenario. 1 oranges.
Sufficient
Ans: "B"
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11. If p is a prime number greater than 2, what is the value of p?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3912.
(1) p is the hundredth prime number. Can be found. Sufficient.
(2) The total number of prime numbers can be found between 1 and 3912. p will be that total. Sufficient.
Ans: "D"
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12. If x is a positive integer, what is the least common multiple of x, 6, and 9?
(1) The LCM of x and 6 is 30.
(2) The LCM of x and 9 is 45.
(1) x can be 5 or 30. LCM=90 for both 5,6,9 and 30,6,9. Sufficient.
(2) x can be 5 or 45. LCM=90 for both 5,6,9 and 45,6,9. Sufficient.
Ans: "D"
Thanks to the author.
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As always please share your way of thinking.
Also you can check new set of PS problems: new-set-of-good-ps-85440.html
_________________
~fluke
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