If a is a 3-digit integer and b is a 3-digit integer, is the units

We are given that a is a 3-digit integer and b is a 3-digit integer and need to determine whether the product of a and b is greater than 5.

Statement One Alone:

The units digit of a is 4.

Statement one alone is not sufficient to answer the question. For example, if the units digit of b is 1, then the units digit of the product of a and b is 4, which is less than 5; however, if the units digit of b is 2, then the units digit of the product of a and b is 8, which is greater than 5.

Statement Two Alone:

The units digit of b is 7.

Statement two alone is not sufficient to answer the question. For example, if the units digit of a is 1, then the units digit of the product of a and b is 7, which is greater than 5; however, if the units digit of a is 0, then the units digit of the product of a and b is 0, which is less than 5.

Statements One and Two Together:

Using the information from statements one and two, we see that since the product of the units digits of a and b is 4 x 7 = 28, the units digit of the product of a and b is 8, which is greater than 5.

Answer: C

We need to find the unit digits of both (or one if its 0).

I - 4 multipels can generate 4 or 8 as two examples - no need to look further. NS

II - 7 multipels can generate 7 or 14, 7>5; 4<5. NS

Together:
4*7=28 8>5. Sufficient.
C

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If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5?

Unit digit of A*B>5
Let x,y = unit digit of a and b

(1) The units digit of a is 4.
If y=2, x*y= 8
If y=1, x*y= 4
NS

(2) The units digit of b is 7
If x= 3, x*y = 21 ( unit digit is 1)
If x= 4, x*y = 28 ( unit digit is 8)
NS

St 1+2. Suff x*y= 28 ( unit digit is 8 )

Option C

a = xyz
b = def
z*f = gh , where h is the unit's digit of z*f
=> h > 5 ?

1) z = 4, f = 1
z*f = 4 => h = 4
NO
But z = 4, f = 2
z*f = 8 => h = 8
YES
Insufficient.


2) f = 7, z = 1
f*z = 7 => h = 7
YES
But, z = 2, f = 7
f*z = 14 => h = 4
NO
Insufficient

1+2)
f = 7 , z = 4
z*f = 28
h > 5 => YES
Sufficient.

C is the answer.

Answer: Option C

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Let a= xyz and b= abc

Units digit of the product of the numbers above will have component of z*c
therefore, question is the unit digit of z*c >5

C: Both statements are necessary.

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