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Math Expert V
Joined: 02 Sep 2009
Posts: 65187
If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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7 00:00

Difficulty:   5% (low)

Question Stats: 88% (00:54) correct 12% (00:55) wrong based on 1245 sessions

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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?

(1) The units digit of a is 4.
(2) The units digit of b is 7.

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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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2
Since we have been asked to find if the units digit of the product of the numbers
is greater than 5, knowing the units digit of both the numbers is enough to determine that.

(1) The units digit of a is 4.
Since, we have no idea about the units digit of the number b, we cannot clearly tell
if the units digit of product is greater than 5. Insufficient
(2) The units digit of b is 7.
Since, we have no idea about the units digit of the number a, we cannot clearly tell
if the units digit of product is greater than 5. Insufficient

On combining both the statements, it is clear that the units digit of their product is 8(>5)
Hence, sufficient(Option C)
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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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Top Contributor
Bunuel wrote:
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?

(1) The units digit of a is 4.
(2) The units digit of b is 7.

Target question: Is the units digit of the product of a and b greater than 5?

Given: a is a 3-digit integer and b is a 3-digit integer

Statement 1: The units digit of a is 4
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 104 and b = 102. In this case the product ab = (104)(102) = ----8. So, the units digit of ab IS greater than 5
Case b: a = 104 and b = 100. In this case the product ab = (104)(100) = ----0. So, the units digit of ab is NOT greater than 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

ASIDE: When I write that the product ab = (104)(102) = ----8, I'm ignoring all digits in the product OTHER THAN the units digit, since that's all we care about.

Statement 2: The units digit of b is 7
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 104 and b = 107. In this case the product ab = (104)(107) = ----8. So, the units digit of ab IS greater than 5
Case b: a = 100 and b = 107. In this case the product ab = (100)(107) = ----0. So, the units digit of ab is NOT greater than 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a = --4
Statement 2 tells us that b = --7
So, ab = (--4)(--7) = -----8
So, the units digit of ab IS greater than 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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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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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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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
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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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Bunuel wrote:
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?

(1) The units digit of a is 4.
(2) The units digit of b is 7.

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.

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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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1
Bunuel wrote:
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?

(1) The units digit of a is 4.
(2) The units digit of b is 7.

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.

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Re: If a is a 3-digit integer and b is a 3-digit integer, is the units  [#permalink]

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_________________ Re: If a is a 3-digit integer and b is a 3-digit integer, is the units   [#permalink] 01 Jun 2020, 19:04

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