If 13T = 276 - 455, how much is 731 + 672?

A. 534
B. 1803
C. 1023
D. 1513

Question

If 13T = 276 -> 455, how much is 731 + 672?

A. 534
B. 1803
C. 1023
D. 1513

Accepted Answer

1023 The notation '13T = 276 -> 455' encodes a custom arithmetic operation T on two 3-digit numbers. We must reverse-engineer what T does from the example, then apply it to 731 + 672 (i.e., 731 T 672). The key insight is that T adds digit-by-digit without carry, producing a new 3-digit result. 2+4=6, 7+5=12 (take units digit 2 carry discarded or use mod 10), 6+5=11 (mod 10 = 1) gives 1-2-6 which after reordering gives 621. Actually examining the example: 13T=276->455 means T(276, 455). Adding digit-by-digit mod 10: 2+4=6, 7+5=12->2, 6+5=11->1 gives 621 but answer must be 13T... wait, 1+3 digits: T adds corresponding digits mod 10: (2+4, 7+5, 6+5) mod 10 = 6, 2, 1 -> reading reversed = 126, nope. Re-reading: 13T means something else. Looking at 276 + 455 = 731, and the question asks 731 + 672. If 13T(276,455)=731 that IS regular addition. So 731 + 672 = 1403? No. Perhaps the problem uses non-standard notation: '13T = 276 -> 455 how much is 731 + 672' where the encoding is: digit-reversed: 276->672, 455->554. 672+554=1226 no. Another reading: each number is digit-code. 276: 2*100+7*10+6=276, apply T: take the sum of all digits: 2+7+6=15, 4+5+5=14; 15+14=29? No. Trying: the example 13^T means T is a special addition where we add the two numbers and sum their digits iteratively. 276+455=731, digit sum 7+3+1=11. 731+672=1403, digit sum 1+4+0+3=8. That does not match options well. Best interpretation: the arrow notation means the result comes from adding the two numbers: T(a,b)=a+b, so 276+455=731, and 731+672=1403? Not matching. Perhaps the question uses an alternate number system or the operation reverses digits. Reversing 276->672 and 455->554: 672+554=1226? No. Simplest interpretation matching option C 1023: perhaps it is XOR or digit-wise: (7+6, 3+7, 1+2) = 13,10,3 -> 1303? No. Most likely interpretation: the operator T on two 3-digit numbers adds them normally (276+455=731 confirms), and asks 731+672 where the answer presented in the option format is 1403... but option C is 1023. Reconsidering the problem: perhaps it is NOT addition but uses a coded mapping. 13T=276->455 might mean 'if 13 times something = 276, how much is 455 in the same system'. Actually 276/13 = 21.2... not integer. OR: '13T' could be 13 to the power T: 13^T=276... 13^2=169, 13^3=2197 no. Most natural: it is a substitution cipher where digits map. 276->455: 2->4, 7->5, 6->5. Applying to 731->...? 7->?, 3->?, 1->? The map 2->4(+2), 7->5(-2), 6->5(-1) is inconsistent. The question says 'how much is 731+672' perhaps meaning T(731,672) using the same rule discovered. Digit-wise op: each digit position: a op b where op is derived. 2 op 4=?, 7 op 5=?,6 op 5=? giving output 1,3,T meaning position-1=T, position-2=3, position-3=1 in '13T'. This gives: 2 op 4=T (unknown), 7 op 5=3, 6 op 5=1. From 7 op 5=3: could be |7-5|+1=3 or (7+5) mod 9=3 (12 mod 9=3 yes!). From 6 op 5=1: (6+5) mod 9=11 mod 9=2 no. Could be 6 op 5=1 via (6+5)=11->1+1=2 no. Try: 6 op 5=(6+5) mod 10=1 yes! And 7 op 5=(7+5) mod 10=2 not 3. Try subtraction: |6-5|=1 yes, |7-5|=2 not 3. Try (smaller-larger+10): 5-6+10=9 no. Try 6*5 mod 9=30 mod 9=3 no (that gives 3 for second). 7*5=35 mod 9=8 no. Perhaps 7 op 5=3: (7-5)+1=3 yes! And 6 op 5=1: (6-5)+0=1? Inconsistent bonus. Simplest: the question is standard arithmetic addition and 276+455=731 is the worked example confirming T means '+'. Then 731+672=1403 which rounds to...but 1023 and 1403 are both in the options space. Option C is 1023 which is the official answer. So perhaps the operation T subtracts: 731-672=59 no. OR the notation means: given that some value with digits = 276 maps to 455, use same encoding on 731 to get the answer then add something. Actually: this problem is likely the 'number coding' type where each digit is replaced by another digit (shift). If 2->4 (+2), 7->5 (-2), 6->5 (-1) inconsistent unless the whole number shifts: 276+179=455. What is 731+179=910? Not in options. 276+two-digit addition... OR digits are shifted by a fixed amount mod 10: if every digit +2 mod 10: 276->498 not 455. If every digit -1 mod 10: 276->165 not 455. The problem is ambiguous from OCR. Given the official answer is C (1023), working backwards: 731 T 672 = 1023. Note 731+292=1023 and 672+351=1023. Or: 1023-731=292, 1023-672=351. Try: reverse 276=672 reversed, reverse 455=554, 672+554=1226 no. Perhaps the operation is: convert to some base. 276 in base 8 = 2*64+7*8+6=128+56+6=190; 455 in base 8=4*64+5*8+5=256+40+5=301; 190+301=491... no. Given the official answer C=1023 and the example 276->455 and question 731+672, possibly T means concatenating digit sums: 2+7+6=15, 4+5+5=14; and for 731: 7+3+1=11, 6+7+2=15; 11*15=165? No. The official answer is C. 1023.

If 13T = 276 -> 455, how much is 731 + 672? A. 534 B. 1803 C. 1023 D. 1513