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If a+5=b+5 what is the value of a + b
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24 Jul 2013, 22:14
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If a+5=b+5 what is the value of a + b? 1) b > 5 and a < 5 2) b = 10
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Re: If a+5=b+5 what is the value of a + b
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25 Jul 2013, 21:53
gmat2805 wrote: If a+5=b+5 what is the value of a + b?
1) b > 5 and a < 5
2) b = 10 Alternatively, you can get rid of the mod sign and then proceed: If a+5=b+5, EITHER a + 5 = b + 5 (In this case a = b) OR a + 5 =  (b + 5) (In this case a + b = 10) 1) b > 5 and a < 5 This statement tells you that a is not equal to b. Then, a + b = 10. Sufficient 2) b = 10 Here a could be 10 so a + b = 20 OR a + b = 10. Not sufficient. Answer (A) Note that a+5=b+5 gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 =  (b + 5) (a + 5) = b + 5 (a + 5) = (b + 5)
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Re: Modulus on both sides
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24 Jul 2013, 22:24
If a+5=b+5 what is the value of a + b? 1) \(b > 5\) and \(a < 5\)if \(b>5\), then \(b+5=b+5\); but \(a<5\) is not enough to determine the sign of \(a+5\), so \(a+5=b+5\), so \(b+5=a+5\) or \(b+5=a5\). In this latter case \(a+b=10\), but in the first one we get \(a=b\). But because a>5 and b<5, \(a=b\) is not a valid option. So only \(a+b=10\) remains. Sufficient 2) b = 10\(a+5=10+5=15\) so \(a=10\)or \(a=20\), not sufficient to determine a+b. A
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Re: If a+5=b+5 what is the value of a + b
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25 Jul 2013, 00:33
gmat2805 wrote: If a+5=b+5 what is the value of a + b?
1) b > 5 and a < 5
2) b = 10 Given that a+5 = b+5. We can square on both sides, as both sides are positive and we get \(\to (a+5)^2(b+5)^2 = 0 \to (a+b+10)(ab)=0\) From F.S 1, we know that \(a \neq{b}\). Thus, only \(a+b+10=0\) and a+b = 10. Sufficient. From F.S 2, we get (a+20)(a10) = 0. Thus, 2 values of a will give 2 different values of (a+b). Insufficient. A.
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Re: If a+5=b+5 what is the value of a + b
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16 May 2015, 20:38
VeritasPrepKarishma wrote: gmat2805 wrote: If a+5=b+5 what is the value of a + b?
1) b > 5 and a < 5
2) b = 10 Alternatively, you can get rid of the mod sign and then proceed: If a+5=b+5, EITHER a + 5 = b + 5 (In this case a = b) OR a + 5 =  (b + 5) (In this case a + b = 10) 1) b > 5 and a < 5 This statement tells you that a is not equal to b. Then, a + b = 10. Sufficient 2) b = 10 Here a could be 10 so a + b = 20 OR a + b = 10. Not sufficient. Answer (A) Note that a+5=b+5 gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 =  (b + 5) (a + 5) = b + 5 (a + 5) = (b + 5) Although you mentioned 4 scenarios , why did just consider 2 of them prior to moving to answer choices



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Re: If a+5=b+5 what is the value of a + b
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17 May 2015, 11:42
Hi All, When DS questions look complex, they often hide subtle patterns. While you might not immediately 'see' what the pattern is, you can do a bit of work (TEST VALUES) and PROVE the pattern exists. Here, we're told that A+5 = B+5. We're asked for the value of A+B. Fact 1: B>5 and A<5 This means that A and B CANNOT be the same number. Let's TEST VALUES and see what happens.... IF... B = 6 A+5 = 11 Since we were told that A<5, A can only have one solution....A = 16 (since 16+5 = 11 = 11). The answer to the question is 6 + (16) = 10 IF... B = 7 A+5 = 12 Since we were told that A<5, A can only have one solution....A = 17 The answer to the question is 7 + (17) = 10 We were NOT told that A and B had to be integers though, so I'll try one more TEST.... IF... B = 5.5 A+5 = 10.5 Since we were told that A<5, A can only have one solution....A = 15.5 The answer to the question is 5.5 + (15.5) = 10 The answer is ALWAYS 10 Fact 1 is SUFFICIENT Fact 2: B = 10 This tells us nothing about the value of A. Fact 2 is INSUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If a+5=b+5 what is the value of a + b
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17 May 2015, 19:30
hak15 wrote: Note that a+5=b+5 gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 =  (b + 5) (a + 5) = b + 5 (a + 5) = (b + 5)
Although you mentioned 4 scenarios , why did just consider 2 of them prior to moving to answer choices The first and the fourth cases give us the same equation: I. a + 5 = b + 5 IV. (a + 5) = (b + 5) Multiply the equation by 1 on both sides to get (a + 5) = (b + 5) The second and third cases give us the same equation: II. (a + 5) = (b + 5) III. (a + 5) = (b + 5) Multiply the equation by 1 on both sides to get (a + 5) = (b + 5) So actually you have only 2 distinct equations.
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Re: If a+5=b+5 what is the value of a + b
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19 May 2015, 21:05
The question can also be solved by basic interpretation of the concept of modulus. Interpreting the Given InfoWe know that modulus denotes the magnitude of the distance of a number from another number. So for a + 5 =  b + 5, we know that distance of a and b from 5 is the same. Thus there are two possible cases: I. a = b. In this case a and b are at the same distance from 5 and thus a + b can take any value II. a and b are on the opposite sides of 5 and equidistant from 5. Let's assume the distance be x. So a = 5 x and b = 5 +x or vice versa. in both the cases we observe that a + b = 10. In other words the question asks us to find if a = b?.StatementIStI tells us that b > 5 and a < 5 i.e. both are distinct numbers. So we know that a + b = 10. Hence stI is sufficient to answer the question StatementIIStII tells us that b = 10. However it does not tell us anything about a. Here a = 10 or a = 20. Hence stII is not sufficient to answer the question. Hope this helps Regards Harsh
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Re: If a+5=b+5 what is the value of a + b
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18 Dec 2016, 01:25
EMPOWERgmatRichC wrote: Hi All, When DS questions look complex, they often hide subtle patterns. While you might not immediately 'see' what the pattern is, you can do a bit of work (TEST VALUES) and PROVE the pattern exists. Here, we're told that A+5 = B+5. We're asked for the value of A+B. Fact 1: B>5 and A<5 This means that A and B CANNOT be the same number. Let's TEST VALUES and see what happens.... IF... B = 6 A+5 = 11 Since we were told that A<5, A can only have one solution....A = 16 (since 16+5 = 11 = 11). The answer to the question is 6 + (16) = 10 IF... B = 7 A+5 = 12 Since we were told that A<5, A can only have one solution....A = 17 The answer to the question is 7 + (17) = 10 We were NOT told that A and B had to be integers though, so I'll try one more TEST.... IF... B = 5.5 A+5 = 10.5 Since we were told that A<5, A can only have one solution....A = 15.5 The answer to the question is 5.5 + (15.5) = 10 The answer is ALWAYS 10 Fact 1 is SUFFICIENT Fact 2: B = 10 This tells us nothing about the value of A. Fact 2 is INSUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich nice explanation, thank you
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Re: If a+5=b+5 what is the value of a + b
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14 Sep 2017, 09:29
Quite Simple Ques by my approach a+5 =  b+5 1) b>5 and a<5 let us say b=6 => a+5 = 11 a+5 = +11 , a=6 ( not possible as a<5) a+5 = 11 , a=16 a+b = 16 +6 =10 if b=7 then a= 17 => a+b =10 A/D can be answer2) b=10 a+5 =15 a=10 or a=20 rejectedA is the answer
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Re: If a+5=b+5 what is the value of a + b
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25 Sep 2018, 12:46
gmat2805 wrote: If a+5=b+5 what is the value of a + b?
1) b > 5 and a < 5
2) b = 10 This question is a great candidate for number picking. If you call b 10, then the second absolute value is 15, meaning that a must be 20 for the first absolute value to also be 15. Thus, a + b could be 10. Then try b = 15. In order to keep the second inequality equal, you’ll have to drop a by 5 to 25, again making the value of a + b = 10. This will hold for all potential values consistent with statement 1, so statement 1 is sufficient. Quote: Additionally you can solve this algebraically with the information in statement 1. If b is positive then you know that b+5=b+5.Logically the only way a + 5 could equal b+5 if a < 0 is if the entire expression on the left is negative. Therefore you know that  (a + 5) = b + 5 and a 5 = b + 5 and a + b = 10. Sufficient. Quote: Statement 2, however, is not sufficient. Knowing that b = 10 means that either a + 5 = 15 or a + 5 = 15, and so with two possible values of a but one exact value of b you cannot solve for a + b, and the correct answer is A.
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Re: If a+5=b+5 what is the value of a + b
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22 Oct 2018, 08:24
gmat2805 wrote: If a+5=b+5 what is the value of a + b?
1) b > 5 and a < 5
2) b = 10 Veritas Prep Official Solution: This question is a great candidate for number picking. If you call b 10, then the second absolute value is 15, meaning that a must be 20 for the first absolute value to also be 15. Thus, a + b could be 10. Then try b = 15. In order to keep the second inequality equal, you’ll have to drop a by 5 to 25, again making the value of a + b = 10. This will hold for all potential values consistent with statement 1, so statement 1 is sufficient. Additionally you can solve this algebraically with the information in statement 1. If b is positive then you know that b+5=b+5 . Logically the only way a + 5 could equal b + 5 if a < 0 is if the entire expression on the left is negative. Therefore you know that  (a + 5) = b + 5 and a 5 = b + 5 and a + b = 10. Sufficient. Statement 2, however, is not sufficient. Knowing that b = 10 means that either a + 5 = 15 or a + 5 = 15, and so with two possible values of a but one exact value of b you cannot solve for a + b, and the correct answer is A.
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