Here is my approach :
1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?(1) x^2+y^2<12
(2) Bonnie and Clyde complete the painting of the car at 10:30am
Ans: x & y are odd integer.
statement1: x=1,y=1 or x=3,y=1 not sufficient
statement2: time of completion is 10.30am-9.45am =45min =3/4Hr; i.e rate and time consumed by both is same.
hence, statement B is sufficient.
Ans : B
2. Is xy<=1/2? (1) x^2+y^2=1
(2) x^2-y^2=0
Ans: statement 1: x^2+y^2=1,i choose the no: x=y=sqrt(1/2); hence sufficient
x=0,y=1 ;hence sufficient
x=1,y=0 ;hence sufficient
i didnt find any number which doesnot comply to statement 1.
so, sufficient.
statement2: x^2-y^2=0 ==> mod(x) = mod(y)
==> x=y
& x=-y not sufficient
Ans: A
3. If a, b and c are integers, is abc an even integer?(1) b is halfway between a and c
(2) a = b - c
Ans: a,b,c are integers,not in sequence.
statement 1: b is half way between a & c.
a=2,b=4,c=6 abc=48 even
a=2,b=3,c=6 abc=36 even
a=3,b=5,c=7 abc=105 odd
statement 1 Not sufficient
Statement 2: a=b-c ==> b=a+c ; we cant say that abc will be even or odd because we dont know whether a,b,c is odd or even.
Not sufficient
on combining both statement also, we cant say anything about abc.
Ans: E.
4. How many numbers of 5 consecutive positive integers is divisible by 4?(1) The median of these numbers is odd
(2) The average (arithmetic mean) of these numbers is a prime number
Ans: E ( No explanation)
5. What is the value of integer x?(1) 2x^2+9<9x
(2) |x+10|=2x+8
Ans:
statement 1: 2x^2+9<9x ==>2x^2-9x+9<0
==>(2x-1)(x-3)<0
so, 1/2<x<3 or x>3&x<1/2
Not sufficient
Statement 2: |x+10| = 2x+8
if x>10;
x+10=2x+8 ==>x=2 but (x>10)
if x<10;
-x-10=2x+8 ==>x= -6 and (x<10)
so, x=-6
Sufficient
Ans B
6. If a and b are integers and ab=2, is a=2?(1) b+3 is not a prime number
(2) a>b
Ans: ab=2 ==> a=2/b
statement 1: b+3 is not a prime number i.e
b+3=1,4,6,8 so, b could be = -2,1,3,5
Not sufficient
Statement 2: a>b
and ab=2 and a&b are integers..only possible value is
a=2 & b=1
Sufficient
Ans B
7. A certain fruit stand sold total of 76 oranges to 19 customers. How many of them bought only one orange?(1) None of the customers bought more than 4 oranges
(2) The difference between the number of oranges bought by any two customers is even
Ans:
total oranges =76
No of customer =19
how many bought only 1 oranges?
statement1:
if none bought more than 4, then,max no of oranges bought is 19x4 =76 oranges.
in short, each customer has bought 4 oranges.
sufficient
statement 2: customer can buy any no of oranges totaling 76. 4-4=0 even, 5-3=2 even,and many more.
not sufficient
Ans : A
8. If x=0.abcd, where a, b, c and d are digits from 0 to 9, inclusive, is x>7/9?(1) a+b>14
(2) a-c>6
Ans: x=0.abcd
7/9=0.777777
statement 1: a+b>14
(a,b)
7,8) ,(7,9),(8,9),(8,8),(9,9)
x=0.abcd ; replacing the value of a&b
x=0.78cd
x=0.79cd
x=0.89cd
x=0.88cd
x=0.99cd
all are greater then 0.77777 hence
Sufficient
statment 2: a-c>6
(a,c): (9,2) (7,0) and many more
x=0.92cd is >0.7777 ok
x=0.70cd is <0.7777 not ok
Not sufficient
Ans A
9. If x and y are negative numbers, is x<y?(1) 3x + 4 < 2y + 3
(2) 2x - 3 < 3y - 4
Ans: x,y <0
statement 1: 3x+4<2y+3 ==>3x-2y+1<0 not sufficient
statement 2: 2x-3<3y-4 ==> 2x-3y +1<0 not sufficient
on combining both statement and solving for x& y
x< -1/5 & y< 1/5
so, y>x for interval (-1/5 to 1/5) since both are -ve so interval should be (-1/5 to 0)
and y=x for (-infinity to -1/5)
Not sufficient
Ans E
10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x?(1) x is a square of an integer
(2) The sum of the distinct prime factors of x is a prime number.
Ans: f(10,x)=11 ==> (10+x)/GCF(10,x) =11 ==>x = GCF(10,x)-10
Statement 1: x could be =1,4,9,16,25..
GCF of (10,1) , (10,4),(10,9) will be different.
Not sufficient
Statement 2:
x= 2 , no of factor 2 (1&2) ok
x= 4 , no of factor 3 (1,2,4) ok
x= 10 , no of factor 4 (1,2,5,10) not ok
not sufficient
on combining I & II
we can get value like 1,4,25 which satisfy both the statement
but no unique value of x can be found.
Ans E
11. If x and y are integers, is x a positive integer?(1) x*|y| is a prime number.
(2) x*|y| is non-negative integer.
Ans:
statement 1: x*|y| is prime no
no information about +ve or -ve no.
Not sufficient
Satement 2: for x*|y| has to non-ve integer both x& y has to -ve or +ve simultaneously
any value inside mode is always positive. mode(y) = positive
to make x*|y| +ve, X has to be positive.
hence sufficient.
Ans B
12. If 6a=3b=7c, what is the value of a+b+c?(1) ac=6b
(2) 5b=8a+4c
Ans: 6a=3b=7c= k
a=k/6
b=k/3
c=k/7
a+b+c = (k/6)+(k/3)+k/7) if we can find the value of K, we wil have our answer.
Statement 1: ac=6b ==>(k/6)(k/7) = 6.k/3 ==>k=84
Sufficient
statement 2: 5b=8a+4c
==> 5.k/3 = (8k/6)+(4.k/7)
no value of k can be found.
Hence
Ans A.
please check my approach ans suggest if anything is missing or wrong.
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