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23 May 2020, 08:41
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If a certain positive two-digit number has tens' digit w and units' digit x, what is the value of w + x ?
(1) 20w + 4x = 44
(2) The product of w and x is 2.
DS20422
Are You Up For the Challenge: 700 Level Questions
(1) 20w + 4x = 44
(2) The product of w and x is 2.
DS20422
Are You Up For the Challenge: 700 Level Questions
23 May 2020, 08:55
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Bunuel
Given: The positive two-digit number has tens' digit w and units' digit x
Since 2-digit numbers do not have 0 in the tens position, we know that w can equal 1, 2, 3, 4, 5, 6, 7, 8 or 9
On the other hand, x can be any of the digits from 0 to 9
Target question: What is the value of w + x ?
Statement 1: 20w + 4x = 44
The first thing we should recognize is that w cannot be greater than 2, since 20w will be greater than 44 for values of w greater than 2.
This means EITHER w = 1 OR w = 2
Let's check each case...
Case a: w = 1.
We get: 20(1) + 4x = 44.
Solve to get: x = 6
So, it could be the case that w = 1 and x = 6, in which case the answer to the target question is w + x = 1 + 6 = 7
Case b: w = 2.
We get: 20(2) + 4x = 44.
Solve to get: x = 1
So, it could be the case that w = 2 and x = 1, in which case the answer to the target question is w + x = 2 + 1 = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The product of w and x is 2
Since w and x are INTEGERS, there are exactly two possible solutions (w = 1 & x = 2 OR w = 2 & x = 1)
Let's examine each possible case:
Case a: w = 1 and x = 2. In this case, the answer to the target question is w + x = 1 + 2 = 3
Case b: w = 2 and x = 1. In this case, the answer to the target question is w + x = 2 + 1 = 3
Since those are the only possible cases, it MUST be the case that w + x = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
General Discussion
yashikaaggarwal
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Updated on: 23 May 2020, 08:56
Originally posted by yashikaaggarwal on 23 May 2020, 08:55.
Last edited by yashikaaggarwal on 23 May 2020, 08:56, edited 1 time in total.
Last edited by yashikaaggarwal on 23 May 2020, 08:56, edited 1 time in total.
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A positive two-digit number has tens' digit w and units' digit x=> 10w+x
what is the value of w + x ?
(1) 20w + 4x = 44
=> 2(10W+2x) = 2(22)
=> 10W+2x = 22 (10w is tens place on which and x is ones. And 22 is made up of two no. 20 as tens and 2 as ones)
=> 10W = 20 & 2x=2
=> W=2 and X=1
Sum of w+x= 2+1= 3(sufficient)
(2) The product of w and x is 2.
Since X and W are in summation no matter there no. There sum will remain same. 1+2=3 & 2+1=3
Let W=-+2 and x = +-1
Case 1: W is -2 and X is -1
Product is -1*-2=2
But sum will be -3
Case 2: W is +2 and X is +1
Product is +1*+2=2
But sum will be +3
There are two different answers from statement 2 (not sufficient)
Answer is A
Posted from my mobile device
what is the value of w + x ?
(1) 20w + 4x = 44
=> 2(10W+2x) = 2(22)
=> 10W+2x = 22 (10w is tens place on which and x is ones. And 22 is made up of two no. 20 as tens and 2 as ones)
=> 10W = 20 & 2x=2
=> W=2 and X=1
Sum of w+x= 2+1= 3(sufficient)
(2) The product of w and x is 2.
Since X and W are in summation no matter there no. There sum will remain same. 1+2=3 & 2+1=3
Let W=-+2 and x = +-1
Case 1: W is -2 and X is -1
Product is -1*-2=2
But sum will be -3
Case 2: W is +2 and X is +1
Product is +1*+2=2
But sum will be +3
There are two different answers from statement 2 (not sufficient)
Answer is A
Posted from my mobile device
