Quiz – 1

(1)--->
let x=3 and y=75
then, x+y= 78 and xy> 60
again if x=-3 and y=75
then, x+y=72 but xy<60
hence, (1) is insufficient.
(2)--->
let x= 3 and y=4
then xy<60
but if x=30 and y=4
then xy>60
hence, (2) is insufficient.


Let us combine (1) and (2).
the least value that any of the two integers can have is 3, in which case the other integer must be at least 58. hence the product will always be more than 60.

So, answer is (C).

Explanation:

since y - 3 = 2,

from 1st we get y = 5 and

since 2nd statement y^{2} = 25

∴ we get y = 5

both the statement are alone sufficient

Explanation:

Since the actual value of the stock before the stock gained the value in the month of June is not known. So, we need some additional data

(1) x is an even number. If x=2 then the answer is YES but if x is any other even number then the answer is NO. Not sufficient.

(2) x can not be divided evenly by an odd number other than 1. This statement implies that x is some power of 2: 2, 4, 8, 16, ... Not sufficient.

(1)+(2) Still not sufficient.

Explanation:

Given that a+b+c = 3,000,000
let a be the smallest account and c be the largest (a<=b<=c),

Is a<500,000

Statement (1) says that the largest is 1,300,000

so now a+b = 1,700,000

There is a possibility for a=b=c (or) a=b (or) b=c, but the largest is 1.3 million so a=b=c can't happen.

However a=b or b=c can happen. This is one choice. But lets say a!=b and b!=c (all three are different)

a+b = 1,700,000

a = 499,000

b=1,201,000

a=501,000

b=1,199,000

we get values for a on either side of 500,000. Hence Statement (1) is not sufficient

Statement (2) says that one of the accounts is $0.7 million.
a+b+c = 3,000,000
lets say b = 0.7 million

a+c=2,300,000

Again we get values of a on either side of 500,000. Hence Statement (2) is not sufficient

Lets combine both

The greatest is 1.3 million and the other one is 0.7 million

which leaves the 1 million for the third account. Hence we can conclusively say that the smallest account is not less than 500,000.

Explanation:

From statement A we know that X⁴ is greater than 3000. There are infinite values for X possible for which X⁴ is greater than 3000

From statement B we know that X⁴ is less than 10,000. This one is a lot better. There are only 9 integer values that satisfy this condition. But this still does not give us a unique answer.

Combining the two statements, we know that 2000 < X⁴ < 10000. The following values of X satisfy this condition -> 8 and 9. Both 8 and 9 are not prime. Hence, the question can be answered conclusively using the two statements. Hence answer choice (C)

From the question, we know that both X and Y are distinct integers and their product is 30.
Explanation:

30 can be obtained as a product of two distinct integers in the following manner

	1 * 30			(-1) * (-30)

	2 * 15			(-2) * (-15)

	3 * 10			(-3) * (-10)

	5 * 6			(-5) * (-6)

Note: in order to divide a number by 6 , that number has to be divisible by both 2 and 3.

Statement 1: m is divisible by 3. No information regarding 2. NOT sufficient.

Statement 2: m is divisible by 4. it means that m is divisible by 2. NO information regarding 3. NOT sufficient.

Combining both statements :

Yes. this what we are looking for . A number is divisible by 6 if it is divisible by both 2 and 3.

The best answer is C.

Explanation:

D because A is not first neither C and B is not the tallest person. The only person will be first is D .

Explanation:

let the speeds be x and y

when moves in same direction the relative speed, x-y = 85-80/37.5 = 0.13 .....(l)

when moves in opposite direction the relative speed, x+y = 165/75 = 2.2...(ll)

now, equation l + equation ll gives, 2x = 0.13+2.2 = 2.33 => x=1.165

from equation l, x-y=0.13 => y = 1.165-0.13 = 1.035

therefore the speeds are 1.165 yards/sec and 1.035 yards/sec.